Pub Date : 2024-06-10DOI: 10.1007/s43034-024-00371-8
D. Mosić
{"title":"Perturbation formulae for the generalized core–EP inverse","authors":"D. Mosić","doi":"10.1007/s43034-024-00371-8","DOIUrl":"https://doi.org/10.1007/s43034-024-00371-8","url":null,"abstract":"","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141362201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-08DOI: 10.1007/s43034-024-00369-2
M. Mabrouk, K. Alahmari, R. Brits
{"title":"Continuous multiplicative spectral functionals on Hermitian Banach algebras","authors":"M. Mabrouk, K. Alahmari, R. Brits","doi":"10.1007/s43034-024-00369-2","DOIUrl":"https://doi.org/10.1007/s43034-024-00369-2","url":null,"abstract":"","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141368370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-03DOI: 10.1007/s43034-024-00362-9
Wenbo Wang, Jixiang Ma, Jianwen Zhou
This article considers the biharmonic equation
$$begin{aligned} Delta ^{2}u=K(x)f(u)quad text {in }~mathbb { R}^{N}. end{aligned}$$
Under suitable assumptions, the existence of positive solutions is obtained. The methods used here contain the integral operator and the Schauder fixed point theory. Since the form of fundamental solution of (Delta ^{2}u=0) in (mathbb {R}^{N}) depends on N, we divide our discussions into three cases as (a) (N=2); (b) (N=4); (c) (N>2) but (Nne 4). The fundamental solution of (Delta ^{2}) plays an essential role in our results.
{"title":"Existence of positive solutions to the biharmonic equations in $$mathbb {R}^{N}$$","authors":"Wenbo Wang, Jixiang Ma, Jianwen Zhou","doi":"10.1007/s43034-024-00362-9","DOIUrl":"https://doi.org/10.1007/s43034-024-00362-9","url":null,"abstract":"<p>This article considers the biharmonic equation </p><span>$$begin{aligned} Delta ^{2}u=K(x)f(u)quad text {in }~mathbb { R}^{N}. end{aligned}$$</span><p>Under suitable assumptions, the existence of positive solutions is obtained. The methods used here contain the integral operator and the Schauder fixed point theory. Since the form of fundamental solution of <span>(Delta ^{2}u=0)</span> in <span>(mathbb {R}^{N})</span> depends on <i>N</i>, we divide our discussions into three cases as (a) <span>(N=2)</span>; (b) <span>(N=4)</span>; (c) <span>(N>2)</span> but <span>(Nne 4)</span>. The fundamental solution of <span>(Delta ^{2})</span> plays an essential role in our results.</p>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-03DOI: 10.1007/s43034-024-00368-3
Denis Fufaev, Evgenij Troitsky
We introduce and study some new uniform structures for Hilbert (C^*)-modules over a (C^*)-algebra (mathcal {A}.) In particular, we prove that in some cases they have the same totally bounded sets. To define one of them, we introduce a new class of (mathcal {A})-functionals: locally adjointable functionals, which have interesting properties in this context and seem to be of independent interest. A relation between these uniform structures and the theory of (mathcal {A})-compact operators is established.
{"title":"A new uniform structure for Hilbert $$C^*$$ -modules","authors":"Denis Fufaev, Evgenij Troitsky","doi":"10.1007/s43034-024-00368-3","DOIUrl":"https://doi.org/10.1007/s43034-024-00368-3","url":null,"abstract":"<p>We introduce and study some new uniform structures for Hilbert <span>(C^*)</span>-modules over a <span>(C^*)</span>-algebra <span>(mathcal {A}.)</span> In particular, we prove that in some cases they have the same totally bounded sets. To define one of them, we introduce a new class of <span>(mathcal {A})</span>-functionals: locally adjointable functionals, which have interesting properties in this context and seem to be of independent interest. A relation between these uniform structures and the theory of <span>(mathcal {A})</span>-compact operators is established.</p>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-03DOI: 10.1007/s43034-024-00370-9
K. A. Makarov, E. Tsekanovskii
This paper presents a solution to the Jørgensen–Muhly problem for a homogeneous symmetric operator with deficiency indices (1, 1) that does not admit a homogeneous self-adjoint extension. Based on the Livšic function approach, we characterize the set of all the solutions of the Jørgensen–Muhly problem up to unitary equivalence and describe the complete set of the corresponding unitary invariants.
{"title":"The Livšic function of a homogeneous symmetric operator and the multiplication theorem","authors":"K. A. Makarov, E. Tsekanovskii","doi":"10.1007/s43034-024-00370-9","DOIUrl":"https://doi.org/10.1007/s43034-024-00370-9","url":null,"abstract":"<p>This paper presents a solution to the Jørgensen–Muhly problem for a homogeneous symmetric operator with deficiency indices (1, 1) that <b>does not admit</b> a homogeneous self-adjoint extension. Based on the Livšic function approach, we characterize the set of all the solutions of the Jørgensen–Muhly problem up to unitary equivalence and describe the complete set of the corresponding unitary invariants.</p>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-23DOI: 10.1007/s43034-024-00361-w
A. Bikchentaev, M. F. Darwish, M. A. Muratov
{"title":"Ideal spaces of measurable operators affiliated to a semifinite von Neumann algebra. II","authors":"A. Bikchentaev, M. F. Darwish, M. A. Muratov","doi":"10.1007/s43034-024-00361-w","DOIUrl":"https://doi.org/10.1007/s43034-024-00361-w","url":null,"abstract":"","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141104343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-23DOI: 10.1007/s43034-024-00358-5
Alain Connes
We compute the full asymptotic expansion of the heat kernel (textrm{Tr}(exp (-tD^2))) where D is, assuming RH, the self-adjoint operator whose spectrum is formed of the imaginary parts of non-trivial zeros of the Riemann zeta function. The coefficients of the expansion are explicit expressions involving Bernoulli and Euler numbers. We relate the divergent terms with the heat kernel expansion of the Dirac square root of the prolate wave operator investigated in our joint work with Henri Moscovici.
我们计算了热核 (textrm{Tr}(exp (-tD^2)))的完全渐近展开，其中 D 是假设为 RH 的自联合算子，其频谱由黎曼 zeta 函数非三维零点的虚部构成。展开的系数是涉及伯努利数和欧拉数的明确表达式。我们将发散项与我们与亨利-莫斯科维奇（Henri Moscovici）合作研究的凸面波算子的狄拉克平方根的热核展开联系起来。
{"title":"Heat expansion and zeta","authors":"Alain Connes","doi":"10.1007/s43034-024-00358-5","DOIUrl":"https://doi.org/10.1007/s43034-024-00358-5","url":null,"abstract":"<p>We compute the full asymptotic expansion of the heat kernel <span>(textrm{Tr}(exp (-tD^2)))</span> where <i>D</i> is, assuming RH, the self-adjoint operator whose spectrum is formed of the imaginary parts of non-trivial zeros of the Riemann zeta function. The coefficients of the expansion are explicit expressions involving Bernoulli and Euler numbers. We relate the divergent terms with the heat kernel expansion of the Dirac square root of the prolate wave operator investigated in our joint work with Henri Moscovici.</p>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-23DOI: 10.1007/s43034-024-00360-x
Marat Pliev, Nariman Abasov, Nonna Dzhusoeva
In this paper, we introduce a new class of regular orthogonally additive operators defined on a lattice-normed space ((mathcal {X},E)) and taking values in a vector lattice F. We show that the vector space (mathcal{O}mathcal{A}_r(mathcal {X},F)) of all regular orthogonally additive operators from a d-decomposable lattice-normed space ((mathcal {X},E)) to a Dedekind complete vector lattice F is a Dedekind complete vector lattice and the lattice operations can be calculated by the Riesz–Kantorovich formulas. We find necessary and sufficient conditions for an orthogonally additive operator (T:mathcal {X}rightarrow F) to be dominated and obtain a criterion of the positivity of a nonlinear superposition operator (T_N:E(X)rightarrow E) defined on Köthe–Bochner space E(X) and taking values in Köthe-*Banach space E. Finally, we state some open problems.
{"title":"The lateral order on Köthe–Bochner spaces and orthogonally additive operators","authors":"Marat Pliev, Nariman Abasov, Nonna Dzhusoeva","doi":"10.1007/s43034-024-00360-x","DOIUrl":"https://doi.org/10.1007/s43034-024-00360-x","url":null,"abstract":"<p>In this paper, we introduce a new class of regular orthogonally additive operators defined on a lattice-normed space <span>((mathcal {X},E))</span> and taking values in a vector lattice <i>F</i>. We show that the vector space <span>(mathcal{O}mathcal{A}_r(mathcal {X},F))</span> of all regular orthogonally additive operators from a <i>d</i>-decomposable lattice-normed space <span>((mathcal {X},E))</span> to a Dedekind complete vector lattice <i>F</i> is a Dedekind complete vector lattice and the lattice operations can be calculated by the Riesz–Kantorovich formulas. We find necessary and sufficient conditions for an orthogonally additive operator <span>(T:mathcal {X}rightarrow F)</span> to be dominated and obtain a criterion of the positivity of a nonlinear superposition operator <span>(T_N:E(X)rightarrow E)</span> defined on Köthe–Bochner space <i>E</i>(<i>X</i>) and taking values in Köthe-*Banach space <i>E</i>. Finally, we state some open problems.</p>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141166350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-17DOI: 10.1007/s43034-024-00363-8
Shengwen Liu, Chen Zhang, Pengtao Li
{"title":"Harmonic functions with traces in Q type spaces related to weights","authors":"Shengwen Liu, Chen Zhang, Pengtao Li","doi":"10.1007/s43034-024-00363-8","DOIUrl":"https://doi.org/10.1007/s43034-024-00363-8","url":null,"abstract":"","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140965239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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