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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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
Dixmier-type traces on symmetric spaces associated with semifinite von Neumann algebras 与半有限 von Neumann 对象相关的对称空间上的 Dixmier 型痕迹
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-04-16 DOI: 10.1007/s43034-024-00343-y
Galina Levitina, Alexandr Usachev
{"title":"Dixmier-type traces on symmetric spaces associated with semifinite von Neumann algebras","authors":"Galina Levitina,&nbsp;Alexandr Usachev","doi":"10.1007/s43034-024-00343-y","DOIUrl":"10.1007/s43034-024-00343-y","url":null,"abstract":"<div><p>We prove that a normalised linear functional on certain symmetric spaces associated with a semifinite von Neumann algebra, respects tail majorisation if and only if it is a Dixmier-type trace.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586699","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
New properties and existence of exact phase-retrievable g-frames 精确相位可检索 g 帧的新特性和存在性
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-04-15 DOI: 10.1007/s43034-024-00345-w
Miao He, Jingsong Leng
{"title":"New properties and existence of exact phase-retrievable g-frames","authors":"Miao He,&nbsp;Jingsong Leng","doi":"10.1007/s43034-024-00345-w","DOIUrl":"10.1007/s43034-024-00345-w","url":null,"abstract":"<div><p>Due to the frame elements of the g-frames being operators, it has many differences from traditional frames. Hence some new characterizations of exact phase-retrievable g-frames from the perspective of operator theory are mainly discussed in this paper. Firstly, we find that for an exact phase-retrievable g-frame, its canonical dual frame will maintain the exact phase-retrievability. Then the stability of the exact phase-retrievability is discussed. More specifically, an exact phase-retrievable g-frame is still exact phase-retrievable after a small disturbance can be obtained in this paper. In addition, we show that the direct sum of two g-frames which have the exact PR-redundancy property also have the exact PR-redundancy property. With the help of these results, the existence of the exact phase-retrievable g-frames is discussed. We prove that for the real Hilbert space case, an exact phase-retrievable g-frame of length <i>N</i> exists for every <span>(2n-1le N le frac{n(n+1)}{2}.)</span></p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586698","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
Normalized solutions of linear and nonlinear coupled Choquard systems with potentials 带电势的线性和非线性耦合 Choquard 系统的归一化解
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-04-15 DOI: 10.1007/s43034-024-00348-7
Zhenyu Guo, Wenyan Jin
{"title":"Normalized solutions of linear and nonlinear coupled Choquard systems with potentials","authors":"Zhenyu Guo,&nbsp;Wenyan Jin","doi":"10.1007/s43034-024-00348-7","DOIUrl":"10.1007/s43034-024-00348-7","url":null,"abstract":"<div><p>In this paper, we study Choquard systems with linear and nonlinear couplings with different potentials under the <span>(L^2)</span>-constraint. We use Ekland variational principle to prove this system has a normalized radially symmetric solution for <span>(L^2)</span>-subcritical case when the dimension is greater than or equal to 2 without potentials. In addition, a positive solution with prescribed <span>(L^2)</span>-constraint under some appropriate assumptions with the potentials was obtained. The proof is based on the refined energy estimates.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586841","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 the decomposability for sums of complex symmetric operators 论复数对称算子之和的可分解性
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-04-10 DOI: 10.1007/s43034-024-00342-z
Sungeun Jung
{"title":"On the decomposability for sums of complex symmetric operators","authors":"Sungeun Jung","doi":"10.1007/s43034-024-00342-z","DOIUrl":"10.1007/s43034-024-00342-z","url":null,"abstract":"<div><p>In this paper, we study decomposability for sums of complex symmetric operators. As applications, we consider decomposable operator matrices.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586700","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
Some converse problems on the g-Drazin invertibility in Banach algebras 关于巴拿赫代数中 g-Drazin 反演性的一些逆问题
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-04-09 DOI: 10.1007/s43034-024-00344-x
Honglin Zou
{"title":"Some converse problems on the g-Drazin invertibility in Banach algebras","authors":"Honglin Zou","doi":"10.1007/s43034-024-00344-x","DOIUrl":"10.1007/s43034-024-00344-x","url":null,"abstract":"<div><p>The main purpose of this paper is to investigate the converse problems of some well-known results related to the generalized Drazin (g-Drazin for short) inverse in Banach algebras. Let <span>({mathcal {A}})</span> be a Banach algebra and <span>(a,bin {mathcal {A}})</span>. First, we give the relationship between the Drazin (g-Drazin, group) invertibility of <i>a</i>, <i>b</i> and that of the sum <span>(a+b)</span> under certain conditions. Then, for a given polynomial <span>(f(x)in {mathbb {C}}[x])</span>, the g-Drazin invertibility of <i>f</i>(<i>a</i>), <span>(f(a^{d}))</span>, <i>f</i>(<i>ab</i>), <span>(f(1-ab))</span> and <span>(f(a+b))</span> are investigated.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586697","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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