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Banach Journal of Mathematical Analysis最新文献

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$$(p,sigma )$$ -Absolute continuity of Bloch maps $$(p,sigma )$$ -布洛赫映射的绝对连续性
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-04-02 DOI: 10.1007/s43037-024-00337-x
A. Bougoutaia, A. Belacel, O. Djeribia, A. Jiménez-Vargas
{"title":"$$(p,sigma )$$ -Absolute continuity of Bloch maps","authors":"A. Bougoutaia, A. Belacel, O. Djeribia, A. Jiménez-Vargas","doi":"10.1007/s43037-024-00337-x","DOIUrl":"https://doi.org/10.1007/s43037-024-00337-x","url":null,"abstract":"<p>Motivated by new progress in the theory of ideals of Bloch maps, we introduce <span>((p,sigma ))</span>-absolutely continuous Bloch maps with <span>(pin [1,infty ))</span> and <span>(sigma in [0,1))</span> from the complex unit open disc <span>(mathbb {D})</span> into a complex Banach space <i>X</i>. We prove a Pietsch domination/factorization theorem for such Bloch maps that provides a reformulation of some results on both absolutely continuous (multilinear) operators and Lipschitz operators. We also identify the spaces of <span>((p,sigma ))</span>-absolutely continuous Bloch zero-preserving maps from <span>(mathbb {D})</span> into <span>(X^*)</span> under a suitable norm <span>(pi ^{mathcal {B}}_{p,sigma })</span> with the duals of the spaces of <i>X</i>-valued Bloch molecules on <span>(mathbb {D})</span> equipped with the Bloch version of the <span>((p^*,sigma ))</span>-Chevet–Saphar tensor norms.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"41 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140596223","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}
引用次数: 0
Composition operators with closed range on the Dirichlet space 迪里希勒空间上具有封闭范围的合成算子
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-03-30 DOI: 10.1007/s43037-024-00334-0
Guangfu Cao, Li He
{"title":"Composition operators with closed range on the Dirichlet space","authors":"Guangfu Cao, Li He","doi":"10.1007/s43037-024-00334-0","DOIUrl":"https://doi.org/10.1007/s43037-024-00334-0","url":null,"abstract":"<p>It is well known that the composition operator on Hardy or Bergman space has a closed range if and only if its Nevanlinna counting function induces a reverse Carleson measure. Similar conclusion is not available on the Dirichlet space. Specifically, the reverse Carleson measure is not enough to ensure that the range of the corresponding composition operator is closed. However, under certain assumptions, we in this paper set the necessary and sufficient condition for a composition operator on the Dirichlet space to have closed range.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"48 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140596053","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}
引用次数: 0
Approximation semigroups for resolvent maps 解析映射的近似半群
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-03-28 DOI: 10.1007/s43037-024-00336-y
Byoung Jin Choi, Un Cig Ji, Yongdo Lim, Miklós Pálfia
{"title":"Approximation semigroups for resolvent maps","authors":"Byoung Jin Choi, Un Cig Ji, Yongdo Lim, Miklós Pálfia","doi":"10.1007/s43037-024-00336-y","DOIUrl":"https://doi.org/10.1007/s43037-024-00336-y","url":null,"abstract":"<p>In this paper, we extend the results for approximation semigroups for general resolvent maps including various resolvents of maps on a general convex geodesic metric space. For our study, we introduce the notion of (general) resolvent maps which is a generalization of the resolvent maps in Lawson (J Lie Theory 33, 361–376, 2023) and then we prove several useful properties for the resolvent map and construct the approximation semigroups for resolvent maps. We also study the convergence of a proximal point like algorithm for the general resolvent map.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"179 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140313584","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}
引用次数: 0
Measure of non-compactness and limiting interpolation with slowly varying functions 慢变函数的非紧凑性测量和极限插值
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-03-21 DOI: 10.1007/s43037-024-00335-z
Fernando Cobos, Luz M. Fernández-Cabrera, Manvi Grover
{"title":"Measure of non-compactness and limiting interpolation with slowly varying functions","authors":"Fernando Cobos, Luz M. Fernández-Cabrera, Manvi Grover","doi":"10.1007/s43037-024-00335-z","DOIUrl":"https://doi.org/10.1007/s43037-024-00335-z","url":null,"abstract":"<p>We give estimates for the measure of non-compactness of an operator interpolated by the limiting methods involving slowly varying functions. As applications we establish estimates for the measure of non-compactness of operators acting between Lorentz–Karamata spaces.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"29 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204727","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}
引用次数: 0
A numerical range approach to Birkhoff–James orthogonality with applications 伯克霍夫-詹姆斯正交性的数值范围方法及其应用
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-03-21 DOI: 10.1007/s43037-024-00333-1
{"title":"A numerical range approach to Birkhoff–James orthogonality with applications","authors":"","doi":"10.1007/s43037-024-00333-1","DOIUrl":"https://doi.org/10.1007/s43037-024-00333-1","url":null,"abstract":"<h3>Abstract</h3> <p>The main aim of this paper is to provide characterizations of Birkhoff–James orthogonality (BJ-orthogonality in short) in a number of families of Banach spaces in terms of the elements of significant subsets of the unit ball of their dual spaces, which makes the characterizations more applicable. The tool to do so is a fine study of the abstract numerical range and its relation with the BJ-orthogonality. Among other results, we provide a characterization of BJ-orthogonality for spaces of vector-valued bounded functions in terms of the domain set and the dual of the target space, which is applied to get results for spaces of vector-valued continuous functions, uniform algebras, Lipschitz maps, injective tensor products, bounded linear operators with respect to the operator norm and to the numerical radius, multilinear maps, and polynomials. Next, we study possible extensions of the well-known Bhatia–Šemrl theorem on BJ-orthogonality of matrices, showing results in spaces of vector-valued continuous functions, compact linear operators on reflexive spaces, and finite Blaschke products. Finally, we find applications of our results to the study of spear vectors and spear operators. We show that no smooth point of a Banach space can be BJ-orthogonal to a spear vector of <em>Z</em>. As a consequence, if <em>X</em> is a Banach space containing strongly exposed points and <em>Y</em> is a smooth Banach space with dimension at least two, then there are no spear operators from <em>X</em> to <em>Y</em>. Particularizing this result to the identity operator, we show that a smooth Banach space containing strongly exposed points has numerical index strictly smaller than one. These latter results partially solve some open problems.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"295 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204854","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}
引用次数: 0
Lipschitz-free spaces and approximating sequences of projections 无 Lipschitz 空间和近似投影序列
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-03-19 DOI: 10.1007/s43037-024-00332-2
Gilles Godefroy
{"title":"Lipschitz-free spaces and approximating sequences of projections","authors":"Gilles Godefroy","doi":"10.1007/s43037-024-00332-2","DOIUrl":"https://doi.org/10.1007/s43037-024-00332-2","url":null,"abstract":"<p>The Lipschitz-free space <span>({mathcal {F}}(M))</span> has an F.D.D. when <i>M</i> is a separable <span>({mathcal {L}}_1)</span>-Banach space, or when <span>(Msubset {mathbb {R}}^n)</span> is a somewhat regular subset. The interplay between the existence of extension operators for Lipschitz maps and the <span>((pi ))</span>-property in Lipschitz-free spaces is investigated. If <i>M</i> is an arbitrary metric space, then <span>({mathcal {F}}(M))</span> has the <span>((pi ))</span>-property up to a universal logarithmic factor. It follows in particular that the <span>((pi ))</span>-property up to a logarithmic factor fails to imply the approximation property. A list of commented open problems is provided.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"14 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140171052","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}
引用次数: 0
Embedded unbounded order convergent sequences in topologically convergent nets in vector lattices 向量网格中拓扑收敛网的嵌入式无界阶收敛序列
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-03-12 DOI: 10.1007/s43037-024-00329-x
Yang Deng, Marcel de Jeu
{"title":"Embedded unbounded order convergent sequences in topologically convergent nets in vector lattices","authors":"Yang Deng, Marcel de Jeu","doi":"10.1007/s43037-024-00329-x","DOIUrl":"https://doi.org/10.1007/s43037-024-00329-x","url":null,"abstract":"<p>We show that, for a class of locally solid topologies on vector lattices, a topologically convergent net has an embedded sequence that is unbounded order convergent to the same limit. Our result implies, and often improves, many of the known results in this vein in the literature. A study of metrisability and submetrisability of locally solid topologies on vector lattices is included.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"68 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125633","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}
引用次数: 0
The skew commutators of Toeplitz operators or Hankel operators on Hardy spaces 哈代空间上托普利兹算子或汉克尔算子的偏斜换向器
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-03-06 DOI: 10.1007/s43037-024-00330-4
Yongning Li, Hanyi Zheng, Xuanhao Ding
{"title":"The skew commutators of Toeplitz operators or Hankel operators on Hardy spaces","authors":"Yongning Li, Hanyi Zheng, Xuanhao Ding","doi":"10.1007/s43037-024-00330-4","DOIUrl":"https://doi.org/10.1007/s43037-024-00330-4","url":null,"abstract":"<p>Let <i>A</i> and <i>B</i> be two bounded linear operators on a Hilbert space. <i>B</i> is called the skew commutator of <i>A</i> if <span>(_{*}[A, B]=AB-BA^{*}=0.)</span> In this paper, we completely characterize when a Toeplitz operator on the Hardy space is a skew commutator of a Hankel operator and when a Hankel operator on the Hardy space is a skew commutator of a Toeplitz operator. Moreover, we also obtain a necessary and sufficient condition for the product of a Hankel operator and a Toeplitz operator to be self-adjoint on the Hardy space.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"270 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140044788","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}
引用次数: 0
Carleson measures and Berezin-type operators on Fock spaces Fock 空间上的卡列森度量和贝雷津类算子
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-03-04 DOI: 10.1007/s43037-024-00331-3
Lifang Zhou, Dong Zhao, Xiaomin Tang
{"title":"Carleson measures and Berezin-type operators on Fock spaces","authors":"Lifang Zhou, Dong Zhao, Xiaomin Tang","doi":"10.1007/s43037-024-00331-3","DOIUrl":"https://doi.org/10.1007/s43037-024-00331-3","url":null,"abstract":"<p>We characterize (vanishing) Fock–Carleson measures by products of functions in Fock spaces. We also study the boundedness of Berezin-type operators from a weighted Fock space to a Lebesgue space. Due to the special properties of Fock–Carleson measures, the boundedness of Berezin-type operators on Fock spaces is different from the corresponding results on Bergman spaces.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"24 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025626","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}
引用次数: 0
An existence result for a suspension of rigid magnetizable particles 刚性可磁化粒子悬浮液的存在结果
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-03-02 DOI: 10.1007/s43037-024-00328-y
Grigor Nika, Bogdan Vernescu
{"title":"An existence result for a suspension of rigid magnetizable particles","authors":"Grigor Nika, Bogdan Vernescu","doi":"10.1007/s43037-024-00328-y","DOIUrl":"https://doi.org/10.1007/s43037-024-00328-y","url":null,"abstract":"<p>We establish the existence of a weak solution for a strongly coupled, nonlinear Stokes–Maxwell system, originally proposed by Nika and Vernescu (Z Angew Math Phys 71(1):1–19, 2020) in the three-dimensional setting. The model effectively couples the Stokes equation with the quasi-static Maxwell’s equations through the Lorentz force and the Maxwell stress tensor. The proof of existence is premised on: (i) the augmented variational formulation of Maxwell’s equations, (ii) the definition of a new function space for the magnetic induction and the verification of a Poincar’e-type inequality, and (iii) the deployment of the Altman–Shinbrot fixed point theorem when the magnetic Reynolds number, <span>({text {R}_{text {m}}},)</span> is small.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140019501","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}
引用次数: 0
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