Annals of Functional Analysis最新文献

Geometry of the unit ball of ({mathcal {L}}(X,Y^*)) 的单位球的几何 ({mathcal {L}}(X,Y^*))

IF 1 3区数学

Annals of Functional Analysis Pub Date : 2026-05-08 DOI: 10.1007/s43034-026-00516-x

T. S. S. R. K. Rao, Susmita Seal

{"title":"Geometry of the unit ball of ({mathcal {L}}(X,Y^*))","authors":"T. S. S. R. K. Rao, Susmita Seal","doi":"10.1007/s43034-026-00516-x","DOIUrl":"10.1007/s43034-026-00516-x","url":null,"abstract":"<div>In this work, we study the geometry of the unit ball of the space of operators ({mathcal {L}}(X,Y^*)), by considering the projective tensor product (Xhat{otimes }_{pi } Y) as a predual. We prove that if an elementary tensor (rank one operator) of the form (x_0^*otimes y_0^* ) in the unit sphere ( S_{{mathcal {L}}(X,Y^*)}) is a (hbox {weak}^*)-strongly extreme point of the unit ball, then (x_0^*) is (hbox {weak}^*)-strongly extreme point of unit ball of (X^*) and (y_0^*) is (hbox {weak}^*)-strongly extreme point of the unit ball of (Y^*). We show that a similar conclusion holds if the rank one operator is a Namioka point (equivalently, a point of (hbox {weak}^*)-weak continuity for the identity mapping) on the unit sphere of ({mathcal {L}}(X,Y^*)). We also study extremal phenomena in the unit ball of ({mathcal {L}}(X,Y^*)^*). We partly solve the open problem: when does an elementary tensor, whose components are Namioka points, become a Namioka point again? We show that if a point (zin S_{{mathcal {L}}(X,Y^*)^*}) is a (hbox {weak}^*)-strongly extreme point of the unit ball, then (z=xotimes y) for some (hbox {weak}^*)-strongly extreme points (xin S_X) and (yin S_Y), provided the space of compact operators, (mathcal {K}(X,Y^*)) is separating for (Xhat{otimes }_{pi } Y).</div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147830065","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}

引用次数: 0

Formulations of Furstenberg’s (times 2 times 3) conjecture in complex analysis and operator algebras 复分析与算子代数中Furstenberg (times 2 times 3)猜想的表述

IF 1 3区数学

Annals of Functional Analysis Pub Date : 2026-04-21 DOI: 10.1007/s43034-026-00512-1

Peter Burton, Jane Panangaden

{"title":"Formulations of Furstenberg’s (times 2 times 3) conjecture in complex analysis and operator algebras","authors":"Peter Burton, Jane Panangaden","doi":"10.1007/s43034-026-00512-1","DOIUrl":"10.1007/s43034-026-00512-1","url":null,"abstract":"<div>Furstenberg’s (times 2 times 3) conjecture has remained a central open problem in ergodic theory for over 50 years, and it serves as the basic test case for a broad class of rigidity phenomena which are believed to hold in number-theoretic dynamics. More recently, two related statements have appeared in the literature: a question about periodic approximation raised by Levit and Vigdorovich in the context of approximate group theory and a periodic equidistribution conjecture formulated by Lindenstrauss. The purpose of this article is to provide equivalent formulations for these three statements in a complex-analytic setting and an operator-algebraic setting, giving nine conjectures grouped into three triples. The complex-analytic conjectures involve so-called Carathéodory functions on the unit disk that satisfy a certain functional identity, and we find that Furstenberg’s conjecture is equivalent to the assertion that every such function is a convex combination of rational functions. The operator-algebraic conjectures involve tracial states on the full group (C^*)-algebra of a certain semidirect product, which is related to Baumslag–Solitar groups.\u0000</div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738100","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}

引用次数: 0

Variable Hajłasz–Besov–Triebel–Lizorkin spaces and capacities in metric measure spaces 在公制度量空间中可变的Hajłasz-Besov-Triebel-Lizorkin空间和容量

IF 1 3区数学

Annals of Functional Analysis Pub Date : 2026-04-17 DOI: 10.1007/s43034-026-00510-3

Ziwei Li, Ciqiang Zhuo

引用次数: 0

Derivation of operator ideals in Banach spaces 巴拿赫空间中算子理想的推导

IF 1 3区数学

Annals of Functional Analysis Pub Date : 2026-04-15 DOI: 10.1007/s43034-026-00511-2

Jesús M. F. Castillo, Ricardo García, Yolanda Moreno Salguero

引用次数: 0

Tauberian pairs of closed subspaces of a Banach space Banach空间的闭子空间的Tauberian对

IF 1 3区数学

Annals of Functional Analysis Pub Date : 2026-04-13 DOI: 10.1007/s43034-026-00514-z

Manuel González, Antonio Martínez-Abejón

引用次数: 0

Tensor products of measurable Banach bundles 可测Banach束的张量积

IF 1 3区数学

Annals of Functional Analysis Pub Date : 2026-04-01 DOI: 10.1007/s43034-026-00494-0

Milica Caković, Danka Lučić, Enrico Pasqualetto

{"title":"Tensor products of measurable Banach bundles","authors":"Milica Caković, Danka Lučić, Enrico Pasqualetto","doi":"10.1007/s43034-026-00494-0","DOIUrl":"10.1007/s43034-026-00494-0","url":null,"abstract":"<div>We study injective and projective tensor products of measurable Banach bundles. More precisely, given two separable measurable Banach bundles (textbf{E}), (textbf{F}) defined over a probability space ((textrm{X},Sigma ,mathfrak {m})), we construct two measurable Banach bundles (textbf{E}hat{otimes }_varepsilon textbf{F}) and (textbf{E}hat{otimes }_pi textbf{F}) over ((textrm{X},Sigma ,mathfrak {m})), such that (Gamma (textbf{E}hat{otimes }_varepsilon textbf{F})cong Gamma (textbf{E})hat{otimes }_varepsilon Gamma (textbf{F})) and (Gamma (textbf{E}hat{otimes }_pi textbf{F})cong Gamma (textbf{E})hat{otimes }_pi Gamma (textbf{F})), where (textbf{G}mapsto Gamma (textbf{G})) is the map assigning to a measurable Banach bundle (textbf{G}) and its space of (L^infty (mathfrak {m}))-sections, while (Gamma (textbf{E})hat{otimes }_varepsilon Gamma (textbf{F})) and (Gamma (textbf{E})hat{otimes }_pi Gamma (textbf{F})) denote the injective and projective tensor products, respectively, of (Gamma (textbf{E})) and (Gamma (textbf{F})) in the sense of (L^infty (mathfrak {m}))-Banach (L^infty (mathfrak {m}))-modules. In combination with previous results, this provides a fiberwise representation of the injective tensor product (mathscr {M}hat{otimes }_varepsilon mathscr {N}) and the projective tensor product (mathscr {M}hat{otimes }_pi mathscr {N}) of two countably generated (L^infty (mathfrak {m}))-Banach (L^infty (mathfrak {m}))-modules (mathscr {M}), (mathscr {N}).</div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-026-00494-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147606842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rokhlin dimension and inductive limit actions on AF-algebras af -代数上的Rokhlin维数与归纳极限作用

IF 1 3区数学

Annals of Functional Analysis Pub Date : 2026-03-28 DOI: 10.1007/s43034-026-00502-3

Sureshkumar Mariappan, Prahlad Vaidyanathan

引用次数: 0

Forelli–Rudin-type operators on tube domains over the realification of the Siegel upper half-space 西格尔上半空间实现上管域上的forelli - rudin型算子

IF 1 3区数学

Annals of Functional Analysis Pub Date : 2026-03-25 DOI: 10.1007/s43034-026-00508-x

Jiaxin Liu, Guan-Tie Deng

引用次数: 0

Min-phase-isometries on complex normed spaces 复赋范空间上的最小相位等距

IF 1 3区数学

Annals of Functional Analysis Pub Date : 2026-03-18 DOI: 10.1007/s43034-026-00503-2

Dongni Tan, Xiaoyong Han, Xujian Huang

{"title":"Min-phase-isometries on complex normed spaces","authors":"Dongni Tan, Xiaoyong Han, Xujian Huang","doi":"10.1007/s43034-026-00503-2","DOIUrl":"10.1007/s43034-026-00503-2","url":null,"abstract":"<div>Let X and Y be complex normed spaces. A mapping (f:Xrightarrow Y) is called a min-phase-isometry with respect to (mathbb {T}_n) if <div><div>$$begin{aligned} min { Vert f(x) - lambda f(y)Vert :lambda in mathbb {T}_n}= min {Vert x - lambda yVert :lambda in mathbb {T}_n}quad (x, y in X), end{aligned}$$</div></div>where (mathbb {T}_n:={textrm{e}^{ifrac{2kpi }{n}}:k = 1,dots ,n}) as the set of the n-th roots of unity. We show that if a surjective min-phase-isometry f has the Max-Functional-Equality Property (MFEP), meaning that for every norm-attaining functional (phi ) of (S_{X^*}), there exists (varphi in S_{Y^*}) such that <div><div>$$begin{aligned} max {textrm{Re},varphi (lambda f(x)) : lambda in mathbb {T}_n} = max {textrm{Re} ,phi (lambda x) : lambda in mathbb {T}_n} end{aligned}$$</div></div>for all (xin X), then for (nge 3) there exists a phase-function (sigma : X rightarrow mathbb {T}_n) such that the mapping (sigma cdot f) is a linear or an anti-linear isometry. Furthermore, we show that if X and Y are smooth spaces, then every surjective min-phase-isometry f has the MFEP.</div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559943","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}

引用次数: 0

Triebel–Lizorkin spaces in Dunkl setting Dunkl环境中的triiebel - lizorkin空间

IF 1 3区数学

Annals of Functional Analysis Pub Date : 2026-03-16 DOI: 10.1007/s43034-026-00509-w

Chuhan Sun, Zhiming Wang

引用次数: 0