Pub Date : 2026-01-22DOI: 10.1016/j.jfa.2026.111367
Ruowei Li , Florentin Münch
In this paper, we prove the convergence and uniqueness of a general discrete-time nonlinear Markov chain with specific conditions. The results have important applications in discrete differential geometry. First, we prove the discrete-time Ollivier Ricci curvature flow converges to a constant curvature metric on a finite weighted graph. As shown in [30, Theorem 5.1], a Laplacian separation principle holds on a locally finite graph with nonnegative Ollivier curvature. We further prove that the Laplacian separation flow converges to the constant Laplacian solution and generalizes the result to nonlinear p-Laplace operators. Moreover, our results can also be applied to study the long-time behavior in the nonlinear Dirichlet forms theory and nonlinear Perron-Frobenius theory. Finally, we define the Ollivier Ricci curvature of the nonlinear Markov chain which is consistent with the classical Ollivier Ricci curvature, sectional curvature [5], coarse Ricci curvature on hypergraphs [14] and the modified Ollivier Ricci curvature for p-Laplace. We also establish the convergence results for the nonlinear Markov chain with nonnegative Ollivier Ricci curvature.
{"title":"The convergence and uniqueness of a discrete-time nonlinear Markov chain","authors":"Ruowei Li , Florentin Münch","doi":"10.1016/j.jfa.2026.111367","DOIUrl":"10.1016/j.jfa.2026.111367","url":null,"abstract":"<div><div>In this paper, we prove the convergence and uniqueness of a general discrete-time nonlinear Markov chain with specific conditions. The results have important applications in discrete differential geometry. First, we prove the discrete-time Ollivier Ricci curvature flow <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>≔</mo><mo>(</mo><mn>1</mn><mo>−</mo><mi>α</mi><msub><mrow><mi>κ</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub><mo>)</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> converges to a constant curvature metric on a finite weighted graph. As shown in <span><span>[30, Theorem 5.1]</span></span>, a Laplacian separation principle holds on a locally finite graph with nonnegative Ollivier curvature. We further prove that the Laplacian separation flow converges to the constant Laplacian solution and generalizes the result to nonlinear <em>p</em>-Laplace operators. Moreover, our results can also be applied to study the long-time behavior in the nonlinear Dirichlet forms theory and nonlinear Perron-Frobenius theory. Finally, we define the Ollivier Ricci curvature of the nonlinear Markov chain which is consistent with the classical Ollivier Ricci curvature, sectional curvature <span><span>[5]</span></span>, coarse Ricci curvature on hypergraphs <span><span>[14]</span></span> and the modified Ollivier Ricci curvature for <em>p</em>-Laplace. We also establish the convergence results for the nonlinear Markov chain with nonnegative Ollivier Ricci curvature.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 9","pages":"Article 111367"},"PeriodicalIF":1.6,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.1016/j.jfa.2026.111359
Rodrigo Bañuelos , Daesung Kim , Mateusz Kwaśnicki
This paper investigates higher dimensional versions of the longstanding conjecture verified in [11] that the -norm of the discrete Hilbert transform on the integers is the same as the -norm of the Hilbert transform on the real line. It computes the -norms of a family of discrete operators on the lattice , . They are discretizations of a new class of singular integrals on that have the same kernels as the classical Riesz transforms near zero and similar behavior at infinity. The discrete operators have the same p-norms as the classical Riesz transforms on . They are constructed as conditional expectations of martingale transforms of Doob h-processes conditioned to exit the upper-half space only on the lattice . The paper also presents a discrete analogue of the classical method of rotations which gives the norm of a different variant of discrete Riesz transforms on . Along the way a new proof is given based on Fourier transform techniques of the key identity used to identify the norm of the discrete Hilbert transform in [11]. Open problems are stated.
{"title":"Sharp ℓp inequalities for discrete singular integrals on the lattice Zd","authors":"Rodrigo Bañuelos , Daesung Kim , Mateusz Kwaśnicki","doi":"10.1016/j.jfa.2026.111359","DOIUrl":"10.1016/j.jfa.2026.111359","url":null,"abstract":"<div><div>This paper investigates higher dimensional versions of the longstanding conjecture verified in <span><span>[11]</span></span> that the <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-norm of the discrete Hilbert transform on the integers is the same as the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-norm of the Hilbert transform on the real line. It computes the <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-norms of a family of discrete operators on the lattice <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, <span><math><mi>d</mi><mo>≥</mo><mn>1</mn></math></span>. They are discretizations of a new class of singular integrals on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> that have the same kernels as the classical Riesz transforms near zero and similar behavior at infinity. The discrete operators have the same <em>p</em>-norms as the classical Riesz transforms on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. They are constructed as conditional expectations of martingale transforms of Doob h-processes conditioned to exit the upper-half space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> only on the lattice <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. The paper also presents a discrete analogue of the classical method of rotations which gives the norm of a different variant of discrete Riesz transforms on <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. Along the way a new proof is given based on Fourier transform techniques of the key identity used to identify the norm of the discrete Hilbert transform in <span><span>[11]</span></span>. Open problems are stated.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 9","pages":"Article 111359"},"PeriodicalIF":1.6,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146057598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.1016/j.jfa.2026.111375
Luca Seemungal, Ben Sharp
We prove a linear upper bound on the Morse index of closed constant mean curvature (CMC) surfaces in orientable three-manifolds in terms of genus, number of branch points and a Willmore-type energy.
{"title":"Index estimates for constant mean curvature surfaces in three-manifolds by energy comparison","authors":"Luca Seemungal, Ben Sharp","doi":"10.1016/j.jfa.2026.111375","DOIUrl":"10.1016/j.jfa.2026.111375","url":null,"abstract":"<div><div>We prove a linear upper bound on the Morse index of closed constant mean curvature (CMC) surfaces in orientable three-manifolds in terms of genus, number of branch points and a Willmore-type energy.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 9","pages":"Article 111375"},"PeriodicalIF":1.6,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146057599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.1016/j.jfa.2026.111379
Yi Gao, Kui Wang
We prove a sharp isoperimetric inequality for the harmonic mean of the first nonzero Neumann eigenvalues for Lipschitz domains symmetric about the origin in Gauss space. Our result generalizes the Szegö-Weinberger type inequality in Gauss space, which was proven by Chiacchio and Di Blasio in [12, Theorem 4.1].
{"title":"An isoperimetric inequality for lower order Neumann eigenvalues in Gauss space","authors":"Yi Gao, Kui Wang","doi":"10.1016/j.jfa.2026.111379","DOIUrl":"10.1016/j.jfa.2026.111379","url":null,"abstract":"<div><div>We prove a sharp isoperimetric inequality for the harmonic mean of the first <span><math><mi>m</mi><mo>−</mo><mn>1</mn></math></span> nonzero Neumann eigenvalues for Lipschitz domains symmetric about the origin in Gauss space. Our result generalizes the Szegö-Weinberger type inequality in Gauss space, which was proven by Chiacchio and Di Blasio in <span><span>[12, Theorem 4.1]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111379"},"PeriodicalIF":1.6,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146074992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.1016/j.jfa.2026.111365
Hongjie Dong , Seongmin Jeon
In this paper, we study solutions u of parabolic systems in divergence form with zero Dirichlet boundary conditions in the upper-half cylinder , where the coefficients are weighted by , . We establish higher-order boundary Schauder type estimates of under the assumption that the coefficients have partially Dini mean oscillation. As an application, we also achieve higher-order boundary Harnack principles for degenerate or singular equations with Hölder continuous coefficients.
{"title":"Degenerate or singular parabolic systems with partially DMO coefficients: the Dirichlet problem","authors":"Hongjie Dong , Seongmin Jeon","doi":"10.1016/j.jfa.2026.111365","DOIUrl":"10.1016/j.jfa.2026.111365","url":null,"abstract":"<div><div>In this paper, we study solutions <em>u</em> of parabolic systems in divergence form with zero Dirichlet boundary conditions in the upper-half cylinder <span><math><msubsup><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span>, where the coefficients are weighted by <span><math><msubsup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math></span>, <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mo>−</mo><mo>∞</mo><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. We establish higher-order boundary Schauder type estimates of <span><math><msubsup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>α</mi></mrow></msubsup><mi>u</mi></math></span> under the assumption that the coefficients have partially Dini mean oscillation. As an application, we also achieve higher-order boundary Harnack principles for degenerate or singular equations with Hölder continuous coefficients.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 9","pages":"Article 111365"},"PeriodicalIF":1.6,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.1016/j.jfa.2026.111364
Jie Liu
In this note, we investigate the stability of self-similar blow-up solutions for superconformal semilinear wave equations in all dimensions. A central aspect of our analysis is the spectral equivalence of the linearized operators under Lorentz transformations in self-similar variables. This observation serves as a useful tool in proving mode stability and provides insights that may aid the study of self-similar solutions in related problems. As a direct consequence, we establish the asymptotic stability of the ODE blow-up family, extending the classical results of Merle and Zaag [45], [51] to the conformal and superconformal regimes and generalizing the recent work of Ostermann [52] to include the entire ODE blow-up family.
{"title":"A note on the stability of self-similar blow-up solutions for superconformal semilinear wave equations","authors":"Jie Liu","doi":"10.1016/j.jfa.2026.111364","DOIUrl":"10.1016/j.jfa.2026.111364","url":null,"abstract":"<div><div>In this note, we investigate the stability of self-similar blow-up solutions for superconformal semilinear wave equations in all dimensions. A central aspect of our analysis is the spectral equivalence of the linearized operators under Lorentz transformations in self-similar variables. This observation serves as a useful tool in proving mode stability and provides insights that may aid the study of self-similar solutions in related problems. As a direct consequence, we establish the asymptotic stability of the ODE blow-up family, extending the classical results of Merle and Zaag <span><span>[45]</span></span>, <span><span>[51]</span></span> to the conformal and superconformal regimes and generalizing the recent work of Ostermann <span><span>[52]</span></span> to include the entire ODE blow-up family.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111364"},"PeriodicalIF":1.6,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.1016/j.jfa.2026.111361
Hang Chen
Let M be an m-dimensional compact Riemannian manifold with boundary. We obtain the upper bounds of the harmonic mean of the first m nonzero Neumann eigenvalues and Steklov eigenvalues involving the conformal volume and relative conformal volume, respectively. We also give an optimal sharp extrinsic upper bound for closed submanifolds in space forms. These extend the previous related results for the first nonzero eigenvalues.
{"title":"Conformal and extrinsic upper bounds for the harmonic mean of Neumann and Steklov eigenvalues","authors":"Hang Chen","doi":"10.1016/j.jfa.2026.111361","DOIUrl":"10.1016/j.jfa.2026.111361","url":null,"abstract":"<div><div>Let <em>M</em> be an <em>m</em>-dimensional compact Riemannian manifold with boundary. We obtain the upper bounds of the harmonic mean of the first <em>m</em> nonzero Neumann eigenvalues and Steklov eigenvalues involving the conformal volume and relative conformal volume, respectively. We also give an optimal sharp extrinsic upper bound for closed submanifolds in space forms. These extend the previous related results for the first nonzero eigenvalues.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111361"},"PeriodicalIF":1.6,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.1016/j.jfa.2026.111360
A. Defant , D. Galicer , M. Mansilla , M. Mastyło , S. Muro
We investigate projection constants for spaces of bihomogeneous harmonic and bihomogeneous polynomials on the unit sphere in finite-dimensional complex Hilbert spaces. Using averaging techniques, we demonstrate that the minimal norm projection aligns with the natural orthogonal projection. This result enables us to establish a connection between these constants and weighted -norms of specific Jacobi polynomials. Consequently, we derive explicit bounds, provide practical expressions for computation, and present asymptotically sharp estimates for these constants. Our findings extend the classical Ryll and Wojtaszczyk formula for the projection constant of homogeneous polynomials in finite-dimensional complex Hilbert spaces to the bihomogeneous setting.
{"title":"Ryll-Wojtaszczyk formulas for bihomogeneous polynomials on the sphere","authors":"A. Defant , D. Galicer , M. Mansilla , M. Mastyło , S. Muro","doi":"10.1016/j.jfa.2026.111360","DOIUrl":"10.1016/j.jfa.2026.111360","url":null,"abstract":"<div><div>We investigate projection constants for spaces of bihomogeneous harmonic and bihomogeneous polynomials on the unit sphere in finite-dimensional complex Hilbert spaces. Using averaging techniques, we demonstrate that the minimal norm projection aligns with the natural orthogonal projection. This result enables us to establish a connection between these constants and weighted <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-norms of specific Jacobi polynomials. Consequently, we derive explicit bounds, provide practical expressions for computation, and present asymptotically sharp estimates for these constants. Our findings extend the classical Ryll and Wojtaszczyk formula for the projection constant of homogeneous polynomials in finite-dimensional complex Hilbert spaces to the bihomogeneous setting.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 9","pages":"Article 111360"},"PeriodicalIF":1.6,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.1016/j.jfa.2026.111363
Daniela De Silva , Seongmin Jeon , Henrik Shahgholian
In this paper, we study superlinear systems that give rise to free boundaries. Such systems appear for example from the minimization of the energy functional but solutions can be also understood in an ad hoc viscosity way.
First, we prove the optimal regularity of minimizers using a variational approach. Then, we apply a linearization technique to establish the -regularity of the “flat” part of the free boundary via a viscosity method. Finally, for minimizing free boundaries, we extend this result to analyticity.
{"title":"The free boundary for a superlinear system","authors":"Daniela De Silva , Seongmin Jeon , Henrik Shahgholian","doi":"10.1016/j.jfa.2026.111363","DOIUrl":"10.1016/j.jfa.2026.111363","url":null,"abstract":"<div><div>In this paper, we study superlinear systems that give rise to free boundaries. Such systems appear for example from the minimization of the energy functional<span><span><span><math><munder><mo>∫</mo><mrow><mi>Ω</mi></mrow></munder><mrow><mo>(</mo><mo>|</mo><mi>∇</mi><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mi>p</mi></mrow></mfrac><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mn>0</mn><mo><</mo><mi>p</mi><mo><</mo><mn>1</mn><mo>,</mo></math></span></span></span> but solutions can be also understood in an ad hoc viscosity way.</div><div>First, we prove the optimal regularity of minimizers using a variational approach. Then, we apply a linearization technique to establish the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span>-regularity of the “flat” part of the free boundary via a viscosity method. Finally, for minimizing free boundaries, we extend this result to analyticity.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111363"},"PeriodicalIF":1.6,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146074901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.1016/j.jfa.2026.111348
Toke Meier Carlsen , Eun Ji Kang
We present an explicit formula for the K-theory of the -algebra associated with a relative generalized Boolean dynamical system . In particular, we find concrete generators for the -group of . We also prove that every gauge-invariant ideal of is Morita equivalent to a -algebra of a relative generalized Boolean dynamical system.
As a structural application, we show that if the underlying Boolean dynamical system satisfies Condition (K), then the associated -algebra is -liftable. Furthermore, we deduce that if is separable and purely infinite, then it has real rank zero.
我们给出了与相对广义布尔动力系统（B，L,θ,Iα；J）相关的C -代数的k理论的一个显式公式。特别地，我们找到了C _ （B，L,θ,Iα；J）的k1群的具体发生器。我们还证明了C （B，L,θ,Iα；J）的每一个规范不变理想都是Morita等价于一个相对广义布尔动力系统的C代数。作为一个结构应用，我们证明了如果底层布尔动力系统（B，L,θ）满足条件(K)，则相关的C -代数是k0可举的。进一步，我们推导出，如果C - C （B，L,θ, i - α；J）是可分离的纯无限的，那么它的实秩为零。
{"title":"K-theory and structural properties of C⁎-algebras associated with relative generalized Boolean dynamical systems","authors":"Toke Meier Carlsen , Eun Ji Kang","doi":"10.1016/j.jfa.2026.111348","DOIUrl":"10.1016/j.jfa.2026.111348","url":null,"abstract":"<div><div>We present an explicit formula for the <em>K</em>-theory of the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra associated with a relative generalized Boolean dynamical system <span><math><mo>(</mo><mi>B</mi><mo>,</mo><mi>L</mi><mo>,</mo><mi>θ</mi><mo>,</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>;</mo><mi>J</mi><mo>)</mo></math></span>. In particular, we find concrete generators for the <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-group of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>B</mi><mo>,</mo><mi>L</mi><mo>,</mo><mi>θ</mi><mo>,</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>;</mo><mi>J</mi><mo>)</mo></math></span>. We also prove that every gauge-invariant ideal of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>B</mi><mo>,</mo><mi>L</mi><mo>,</mo><mi>θ</mi><mo>,</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>;</mo><mi>J</mi><mo>)</mo></math></span> is Morita equivalent to a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra of a relative generalized Boolean dynamical system.</div><div>As a structural application, we show that if the underlying Boolean dynamical system <span><math><mo>(</mo><mi>B</mi><mo>,</mo><mi>L</mi><mo>,</mo><mi>θ</mi><mo>)</mo></math></span> satisfies Condition (K), then the associated <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra is <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-liftable. Furthermore, we deduce that if <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>B</mi><mo>,</mo><mi>L</mi><mo>,</mo><mi>θ</mi><mo>,</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>;</mo><mi>J</mi><mo>)</mo></math></span> is separable and purely infinite, then it has real rank zero.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111348"},"PeriodicalIF":1.6,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146074900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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