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Dunford–Pettis type properties of locally convex spaces 局部凸空间的邓福德-佩提斯类型特性
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-09 DOI: 10.1007/s43034-024-00359-4
Saak Gabriyelyan
{"title":"Dunford–Pettis type properties of locally convex spaces","authors":"Saak Gabriyelyan","doi":"10.1007/s43034-024-00359-4","DOIUrl":"10.1007/s43034-024-00359-4","url":null,"abstract":"<div><p>In 1953, Grothendieck introduced and studied the Dunford–Pettis property (the <span>({textrm{DP}})</span> property) and the strict Dunford–Pettis property (the strict <span>({textrm{DP}})</span> property). The <span>({textrm{DP}})</span> property of order <span>(pin [1,infty ])</span> for Banach spaces was introduced by Castillo and Sanchez in 1993. Being motivated by these notions, for <span>(p,qin [1,infty ],)</span> we define the quasi-Dunford–Pettis property of order <i>p</i> (the quasi <span>({textrm{DP}}_p)</span> property) and the sequential Dunford–Pettis property of order (<i>p</i>, <i>q</i>) (the sequential <span>({textrm{DP}}_{(p,q)})</span> property). We show that a locally convex space (lcs) <i>E</i> has the <span>({textrm{DP}})</span> property if the space <i>E</i> endowed with the Grothendieck topology <span>(tau _{Sigma '})</span> has the weak Glicksberg property, and <i>E</i> has the quasi <span>({textrm{DP}}_p)</span> property if the space <span>((E,tau _{Sigma '}) )</span> has the <i>p</i>-Schur property. We also characterize lcs with the sequential <span>({textrm{DP}}_{(p,q)})</span> property. Some permanent properties and relationships between Dunford–Pettis type properties are studied. Numerous (counter)examples are given. In particular, we give the first example of an lcs with the strict <span>({textrm{DP}})</span> property but without the <span>({textrm{DP}})</span> property and show that the completion of even normed spaces with the <span>({textrm{DP}})</span> property may not have the <span>({textrm{DP}})</span> property.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925522","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
Banach spaces of sequences arising from infinite matrices 由无限矩阵产生的序列的巴拿赫空间
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-08 DOI: 10.1007/s43034-024-00356-7
A. Bërdëllima, N. L. Braha
{"title":"Banach spaces of sequences arising from infinite matrices","authors":"A. Bërdëllima,&nbsp;N. L. Braha","doi":"10.1007/s43034-024-00356-7","DOIUrl":"10.1007/s43034-024-00356-7","url":null,"abstract":"<div><p>Given an infinite matrix <span>(M=(m_{nk}))</span>, we study a family of sequence spaces <span>(ell _M^p)</span> associated with it. When equipped with a suitable norm <span>(Vert cdot Vert _{M,p})</span>, we prove some basic properties of the Banach spaces of sequences <span>((ell _M^p,Vert cdot Vert _{M,p}))</span>. In particular, we show that such spaces are separable and strictly/uniformly convex for a considerably large class of infinite matrices <i>M</i> for all <span>(p&gt;1)</span>. A special attention is given to the identification of the dual space <span>((ell _M^p )^*)</span>. Building on the earlier works of Bennett and Jägers, we extend and apply some classical factorization results to the sequence spaces <span>(ell _M^p)</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925521","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
Geometric properties for a class of deformed trace functions 一类变形痕量函数的几何特性
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-08 DOI: 10.1007/s43034-024-00353-w
Frank Hansen
{"title":"Geometric properties for a class of deformed trace functions","authors":"Frank Hansen","doi":"10.1007/s43034-024-00353-w","DOIUrl":"10.1007/s43034-024-00353-w","url":null,"abstract":"<div><p>We investigate the geometric properties for a class of trace functions expressed in terms of the deformed logarithmic and exponential functions. We extend earlier results of Epstein, Hiai, Carlen and Lieb.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00353-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925309","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
On conjugations concerning idempotents 关于幂函数的共轭
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-06 DOI: 10.1007/s43034-024-00354-9
Xiao-Ming Xu, Yi Yuan, Yuan Li, Yong Chen
{"title":"On conjugations concerning idempotents","authors":"Xiao-Ming Xu,&nbsp;Yi Yuan,&nbsp;Yuan Li,&nbsp;Yong Chen","doi":"10.1007/s43034-024-00354-9","DOIUrl":"10.1007/s43034-024-00354-9","url":null,"abstract":"<div><p>We introduce the <i>C</i>-decomposition property for reducible bounded linear operators on a Hilbert space, and prove that an arbitrary idempotent operator has the <i>C</i>-decomposition property with respect to a particular space decomposition, which is related to Halmos’ two projections theory. Using this, we obtain a general explicit description for all the conjugations <i>C</i> such that a given idempotent operator is a <i>C</i>-projection. We also present a characterization of the ranges of <i>C</i>-projections for any conjugation <i>C</i>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886018","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
Estimates of discrete Riesz potentials on discrete weighted Lebesgue spaces 离散加权勒贝格空间上离散里兹势的估算
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-05 DOI: 10.1007/s43034-024-00357-6
Xuebing Hao, Baode Li, Shuai Yang
{"title":"Estimates of discrete Riesz potentials on discrete weighted Lebesgue spaces","authors":"Xuebing Hao,&nbsp;Baode Li,&nbsp;Shuai Yang","doi":"10.1007/s43034-024-00357-6","DOIUrl":"10.1007/s43034-024-00357-6","url":null,"abstract":"<div><p>Let <span>(0&lt;alpha &lt;1)</span>. We obtain necessary and sufficient conditions for the boundedness of the discrete fractional Hardy–Littlewood maximal operators <span>(mathcal {M}_alpha )</span> on discrete weighted Lebesgue spaces. From this and a discrete variant of the Whitney decomposition theorem, necessary and sufficient conditions for the boundedness of the discrete Riesz potentials <span>(I_alpha )</span> on discrete weighted Lebesgue spaces are discussed. As an application, the boundedness of <span>(I_alpha )</span> on discrete weighted Morrey spaces is further obtained.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886020","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
Complex symmetric Toeplitz operators on the Hardy spaces and Bergman spaces 哈代空间和伯格曼空间上的复对称托普利兹算子
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-02 DOI: 10.1007/s43034-024-00352-x
Xiaohe Hu, Cui Wang, Zhiyuan Xu
{"title":"Complex symmetric Toeplitz operators on the Hardy spaces and Bergman spaces","authors":"Xiaohe Hu,&nbsp;Cui Wang,&nbsp;Zhiyuan Xu","doi":"10.1007/s43034-024-00352-x","DOIUrl":"10.1007/s43034-024-00352-x","url":null,"abstract":"<div><p>In this paper, we first completely characterize the complex symmetric Toeplitz operators <span>(T_varphi )</span> on the Hardy spaces <span>(H^2({mathbb {D}}))</span> with conjugations <span>({mathcal {C}}_p^{i,j})</span> and <span>({mathcal {C}}_n)</span>. Next, we give a method to determine the coefficients of <span>(varphi (z))</span> when <span>(T_varphi )</span> is complex symmetric on <span>(H^2({mathbb {D}}))</span> with the conjugation <span>({mathcal {C}}_sigma )</span>, which partially solves a problem raised by [2]. Finally, we consider the complex symmetric Toeplitz operators <span>(T_varphi )</span> on the weighted Bergman spaces <span>(A^2({mathbb {B}}_{n}))</span> and the pluriharmonic Bergman spaces <span>(b^2({mathbb {B}}_{n}))</span> with conjugations <span>({mathcal {C}}_V)</span>, where <i>V</i> is a symmetric permutation matrix.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886396","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
A categorical approach to injective envelopes 注入包络的分类方法
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-04-23 DOI: 10.1007/s43034-024-00350-z
Arianna Cecco
{"title":"A categorical approach to injective envelopes","authors":"Arianna Cecco","doi":"10.1007/s43034-024-00350-z","DOIUrl":"10.1007/s43034-024-00350-z","url":null,"abstract":"<div><p>We explore functors between operator space categories, some properties of these functors, and establish relations between objects in these categories and their images under these functors, in particular regarding injectivity and injective envelopes. We also compare the purely categorical definition of injectivity with the ‘standard’ operator theoretical definition. An appendix by D. P. Blecher discusses the unitization of an operator space and its injective envelope.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805145","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
On positive operator-valued measures generated by a family of one-dimensional projectors 论一维投影族生成的正算子值度量
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-04-22 DOI: 10.1007/s43034-024-00351-y
G. G. Amosov, A. D. Baranov, D. A. Kronberg
{"title":"On positive operator-valued measures generated by a family of one-dimensional projectors","authors":"G. G. Amosov,&nbsp;A. D. Baranov,&nbsp;D. A. Kronberg","doi":"10.1007/s43034-024-00351-y","DOIUrl":"10.1007/s43034-024-00351-y","url":null,"abstract":"<div><p>We study positive operator-valued measures generated by projections on one-dimensional subspaces. A special attention is paid to the case in which subspaces are spanned by vectors forming a Riesz basis. It is shown that the measurement fulfilled by such measure is informationally complete for quantum states being a convex hull of projections on subspaces spanned by the system of biorthogonal vectors. We also discuss the properties of different quantum channels associated with a discrete measurement. Finally, we show that our measurement allows to introduce a quantum instrument taking values in the set of two points.\u0000</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140676564","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
Schur inequality for Murray–von Neumann algebras and its applications 墨累-冯-诺依曼代数的舒尔不等式及其应用
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-04-18 DOI: 10.1007/s43034-024-00347-8
Shavkat Ayupov, Jinghao Huang, Karimbergen Kudaybergenov
{"title":"Schur inequality for Murray–von Neumann algebras and its applications","authors":"Shavkat Ayupov,&nbsp;Jinghao Huang,&nbsp;Karimbergen Kudaybergenov","doi":"10.1007/s43034-024-00347-8","DOIUrl":"10.1007/s43034-024-00347-8","url":null,"abstract":"<div><p>In this paper, we present a version of the Schur inequality in the setting of Murray–von Neumann algebras, extending a result by Arveson and Kadison. We also describe the ring isomorphisms between <span>(*)</span>-subalgebras of two Murray–von Neumann algebras. A short proof of the commutator estimation theorem for Murray–von Neumann algebras is given as an easy application.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140624616","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
Toeplitz operators with monomial symbols on the Dirichlet spaces 狄利克空间上具有单项式符号的托普利兹算子
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-04-17 DOI: 10.1007/s43034-024-00346-9
Sumin Kim, Jongrak Lee
{"title":"Toeplitz operators with monomial symbols on the Dirichlet spaces","authors":"Sumin Kim,&nbsp;Jongrak Lee","doi":"10.1007/s43034-024-00346-9","DOIUrl":"10.1007/s43034-024-00346-9","url":null,"abstract":"<div><p>In this paper, we are concerned with the various properties of the Toeplitz operators acting on the Dirichlet spaces. First, we consider the matrix representation of Toeplitz operators with harmonic and monomial symbols. Second, we establish the expansivity and contractivity of the Toeplitz operators <span>(T_{varphi })</span> with monomial symbols <span>(varphi )</span>. Third, we give a necessary and sufficient conditions for the normality and hyponormality of the Toeplitz operators <span>(T_{varphi })</span> with such symbols on the Dirichlet spaces.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140617265","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
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