Pub Date : 2024-08-08DOI: 10.1007/s43034-024-00378-1
Daisuke Hirota, Izuho Matsuzaki, Takeshi Miura
For a locally compact Hausdorff space L, we denote by (C_0(L,{mathbb {R}})) the Banach space of all continuous real-valued functions on L vanishing at infinity equipped with the supremum norm. We prove that every surjective phase-isometry (T:C_0^+(X,{mathbb {R}})rightarrow C_0^+(Y,{mathbb {R}})) between the positive cones of (C_0(X,{mathbb {R}})) and (C_0(Y,{mathbb {R}})) is a composition operator induced by a homeomorphism between X and Y. Furthermore, we show that any surjective phase-isometry (T:C_0^+(X,{mathbb {R}})rightarrow C_0^+(Y,{mathbb {R}})) extends to a surjective linear isometry from (C_0(X,{mathbb {R}})) onto (C_0(Y,{mathbb {R}})).
对于局部紧凑的 Hausdorff 空间 L，我们用 C_0(L,{/mathbb {R}})表示 L 上所有在无穷处消失的连续实值函数的巴纳赫空间（Banach space of all continuous real-valued functions on L vanishing at infinity equipped with the supremum norm）。我们证明了在(C_0(X,{/mathbb {R}}))和(C_0(Y,{/mathbb {R}}))的正锥间的每一个投射相异度（T:C_0^+(X,{/mathbb {R}})rightarrow C_0^+(Y,{/mathbb {R}})）都是由 X 和 Y 之间的同构所诱导的组成算子。此外，我们还证明了任何从 (C_0(X,{mathbb {R}})rightarrow C_0^+(Y,{mathbb {R}}) 扩展到 (C_0(X,{mathbb {R}}) 上的(C_0(Y,{/mathbb {R}}))的投射相等性。）
{"title":"Phase-isometries between the positive cones of the Banach space of continuous real-valued functions","authors":"Daisuke Hirota, Izuho Matsuzaki, Takeshi Miura","doi":"10.1007/s43034-024-00378-1","DOIUrl":"https://doi.org/10.1007/s43034-024-00378-1","url":null,"abstract":"<p>For a locally compact Hausdorff space <i>L</i>, we denote by <span>(C_0(L,{mathbb {R}}))</span> the Banach space of all continuous real-valued functions on <i>L</i> vanishing at infinity equipped with the supremum norm. We prove that every surjective phase-isometry <span>(T:C_0^+(X,{mathbb {R}})rightarrow C_0^+(Y,{mathbb {R}}))</span> between the positive cones of <span>(C_0(X,{mathbb {R}}))</span> and <span>(C_0(Y,{mathbb {R}}))</span> is a composition operator induced by a homeomorphism between <i>X</i> and <i>Y</i>. Furthermore, we show that any surjective phase-isometry <span>(T:C_0^+(X,{mathbb {R}})rightarrow C_0^+(Y,{mathbb {R}}))</span> extends to a surjective linear isometry from <span>(C_0(X,{mathbb {R}}))</span> onto <span>(C_0(Y,{mathbb {R}}))</span>.</p>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948441","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 : 2024-08-08DOI: 10.1007/s43034-024-00381-6
Fritz Gesztesy, Michael M. H. Pang, Jonathan Stanfill
The principal purpose of this note is to prove a logarithmic refinement of the power weighted Hardy–Rellich inequality on n-dimensional balls, valid for the largest variety of underlying parameters and for all dimensions (n in {mathbb {N}}), (nge 2).
本论文的主要目的是证明 n 维球上的幂加权哈代-雷利克不等式的对数改进，它对最大范围的基础参数和所有维度都有效（n in {mathbb {N}}), (nge 2).
{"title":"Logarithmic refinements of a power weighted Hardy–Rellich-type inequality","authors":"Fritz Gesztesy, Michael M. H. Pang, Jonathan Stanfill","doi":"10.1007/s43034-024-00381-6","DOIUrl":"https://doi.org/10.1007/s43034-024-00381-6","url":null,"abstract":"<p>The principal purpose of this note is to prove a logarithmic refinement of the power weighted Hardy–Rellich inequality on <i>n</i>-dimensional balls, valid for the largest variety of underlying parameters and for all dimensions <span>(n in {mathbb {N}})</span>, <span>(nge 2)</span>.</p>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948439","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 : 2024-07-26DOI: 10.1007/s43034-024-00376-3
Yong Jiao, Tiantian Zhao, Dejian Zhou
We study the triangular (theta )-mean of the partial sums of (f in L_{p}({mathbb {T}}_{q}^{2})) and prove the following noncommutative weak and strong type maximal inequalities:
$$begin{aligned} Vert (sigma _n^{Delta ,theta }(f))_{nge 1}Vert _{Lambda _{1,infty }({mathbb {T}}_q^2,ell _{infty })}le c_theta Vert fVert _{L_1({mathbb {T}}_{q}^2)},quad p=1 end{aligned}$$
where ({mathbb {T}}_{q}^{2}) is a 2-dimensional quantum torus. As a consequence, we obtain the bilateral almost uniform convergence of (sigma _n^{Delta ,theta }(f)) provided (f in L_{p}({mathbb {T}}_{q}^{2}).)
{"title":"Triangular- $$theta $$ summability of double Fourier series on quantum tori","authors":"Yong Jiao, Tiantian Zhao, Dejian Zhou","doi":"10.1007/s43034-024-00376-3","DOIUrl":"https://doi.org/10.1007/s43034-024-00376-3","url":null,"abstract":"<p>We study the triangular <span>(theta )</span>-mean of the partial sums of <span>(f in L_{p}({mathbb {T}}_{q}^{2}))</span> and prove the following noncommutative weak and strong type maximal inequalities: </p><span>$$begin{aligned} Vert (sigma _n^{Delta ,theta }(f))_{nge 1}Vert _{Lambda _{1,infty }({mathbb {T}}_q^2,ell _{infty })}le c_theta Vert fVert _{L_1({mathbb {T}}_{q}^2)},quad p=1 end{aligned}$$</span><p>and </p><span>$$begin{aligned} left| left( sigma _{n}^{Delta ,theta }(f)right) _{n ge 1}right| _{L_p({mathbb {T}}_q^2, ell _{infty })} le c_{p, theta }Vert fVert _{L_p({mathbb {T}}_q^2)},quad 1<p<infty , end{aligned}$$</span><p>where <span>({mathbb {T}}_{q}^{2})</span> is a 2-dimensional quantum torus. As a consequence, we obtain the bilateral almost uniform convergence of <span>(sigma _n^{Delta ,theta }(f))</span> provided <span>(f in L_{p}({mathbb {T}}_{q}^{2}).)</span></p>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775687","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 : 2024-07-14DOI: 10.1007/s43034-024-00375-4
Dmitriy Zanin
We provide a semi-constructive criterion for ellipticity of the differential operator on the Heisenberg group (mathbb {H}^1.)
我们提供了一个关于海森堡群 (mathbb {H}^1.) 上微分算子椭圆性的半结构性判据。
{"title":"Criterion for ellipticity on Heisenberg group","authors":"Dmitriy Zanin","doi":"10.1007/s43034-024-00375-4","DOIUrl":"https://doi.org/10.1007/s43034-024-00375-4","url":null,"abstract":"<p>We provide a semi-constructive criterion for ellipticity of the differential operator on the Heisenberg group <span>(mathbb {H}^1.)</span></p>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614069","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}
The article deals with the reduced semigroup (C^*)-algebras for the positive cones in ordered abelian groups. These (C^*)-algebras are generated by the regular isometric representations of the cones. Using the universal property of the isometric representations for the positive cones, we treat the reduced semigroup (C^*)-algebras as the universal (C^*)-algebras which are defined by sets of generators subject to relations. For arbitrary sequences of prime numbers, we consider the ordered groups of rational numbers determined by these sequences and the reduced semigroup (C^*)-algebras of the positive cones in these groups. It is shown that such an algebra can be characterized as a universal (C^*)-algebra generated by a countable set of isometries subject to polynomial relations associated with a sequence of prime numbers.
{"title":"A universal property of semigroup $$C^*$$ -algebras generated by cones in groups of rationals","authors":"Renat Gumerov, Anatoliy Kuklin, Ekaterina Lipacheva","doi":"10.1007/s43034-024-00374-5","DOIUrl":"https://doi.org/10.1007/s43034-024-00374-5","url":null,"abstract":"<p>The article deals with the reduced semigroup <span>(C^*)</span>-algebras for the positive cones in ordered abelian groups. These <span>(C^*)</span>-algebras are generated by the regular isometric representations of the cones. Using the universal property of the isometric representations for the positive cones, we treat the reduced semigroup <span>(C^*)</span>-algebras as the universal <span>(C^*)</span>-algebras which are defined by sets of generators subject to relations. For arbitrary sequences of prime numbers, we consider the ordered groups of rational numbers determined by these sequences and the reduced semigroup <span>(C^*)</span>-algebras of the positive cones in these groups. It is shown that such an algebra can be characterized as a universal <span>(C^*)</span>-algebra generated by a countable set of isometries subject to polynomial relations associated with a sequence of prime numbers.</p>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141571684","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 : 2024-07-01DOI: 10.1007/s43034-024-00377-2
Weiwei Wang
{"title":"Extremals of singular Hardy–Trudinger–Moser inequality with remainder terms on unit disc","authors":"Weiwei Wang","doi":"10.1007/s43034-024-00377-2","DOIUrl":"https://doi.org/10.1007/s43034-024-00377-2","url":null,"abstract":"","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141715896","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 : 2024-06-22DOI: 10.1007/s43034-024-00373-6
Mixuan Hou, Cuiting Li, Guangheng Xie, Yahui Zuo
Let (mathcal {M}) be a semifinite von Neumann algebra and ((mathcal {M}_n)_{nge 0}) a nondecreasing filtration of von Neumann subalgebras of (mathcal {M}). Suppose that (Phi ) is a p-convex and q-concave Orlicz function with (1< ple q <infty ). In this paper, we establish the complex interpolation between the column martingale little BMO space (textrm{bmo}^c(mathcal {M})) and the noncommutative column conditioned martingale Hardy–Orlicz space (h_{Phi }^c(mathcal {M})) associated with the filtration ((mathcal {M}_n)_{nge 0}).
{"title":"Complex interpolation between noncommutative martingale BMO spaces and Hardy–Orlicz spaces","authors":"Mixuan Hou, Cuiting Li, Guangheng Xie, Yahui Zuo","doi":"10.1007/s43034-024-00373-6","DOIUrl":"https://doi.org/10.1007/s43034-024-00373-6","url":null,"abstract":"<p>Let <span>(mathcal {M})</span> be a semifinite von Neumann algebra and <span>((mathcal {M}_n)_{nge 0})</span> a nondecreasing filtration of von Neumann subalgebras of <span>(mathcal {M})</span>. Suppose that <span>(Phi )</span> is a <i>p</i>-convex and <i>q</i>-concave Orlicz function with <span>(1< ple q <infty )</span>. In this paper, we establish the complex interpolation between the column martingale little BMO space <span>(textrm{bmo}^c(mathcal {M}))</span> and the noncommutative column conditioned martingale Hardy–Orlicz space <span>(h_{Phi }^c(mathcal {M}))</span> associated with the filtration <span>((mathcal {M}_n)_{nge 0})</span>.</p>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551645","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 : 2024-06-13DOI: 10.1007/s43034-024-00364-7
Danko R. Jocić, Zora Lj. Golubović, Mihailo Krstić, Stevan Milašinović
{"title":"Norm inequalities for the iterated perturbations of Laplace transformers generated by accretive $$scriptstyle N$$-tuples of operators in Q and Q* ideals of compact operators","authors":"Danko R. Jocić, Zora Lj. Golubović, Mihailo Krstić, Stevan Milašinović","doi":"10.1007/s43034-024-00364-7","DOIUrl":"https://doi.org/10.1007/s43034-024-00364-7","url":null,"abstract":"","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141345490","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 : 2024-06-13DOI: 10.1007/s43034-024-00372-7
Shelley Hebert, S. Klimek, Matt McBride, J. Peoples
{"title":"Crossed product C$$^*$$-algebras associated with p-adic multiplication","authors":"Shelley Hebert, S. Klimek, Matt McBride, J. Peoples","doi":"10.1007/s43034-024-00372-7","DOIUrl":"https://doi.org/10.1007/s43034-024-00372-7","url":null,"abstract":"","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141349677","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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