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Advances in Operator Theory最新文献

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Localized Bishop-Phelps-Bollobás type properties for minimum norm and Crawford number attaining operators 最小范数和克劳福德数获得算子的本地化Bishop-Phelps-Bollobás类型属性
IF 0.8
Advances in Operator Theory Pub Date : 2025-01-13 DOI: 10.1007/s43036-024-00415-9
Uday Shankar Chakraborty
{"title":"Localized Bishop-Phelps-Bollobás type properties for minimum norm and Crawford number attaining operators","authors":"Uday Shankar Chakraborty","doi":"10.1007/s43036-024-00415-9","DOIUrl":"10.1007/s43036-024-00415-9","url":null,"abstract":"<div><p>In this paper, we study the approximate minimizing property (AMp) for operators, a localized Bishop-Phelps-Bollobás type property with respect to the minimum norm. Given Banach spaces <i>X</i> and <i>Y</i> we define a new class <span>(mathcal{A}mathcal{M}(X,Y))</span> of bounded linear operators from <i>X</i> to <i>Y</i> for which the pair (<i>X</i>, <i>Y</i>) satisfies the AMp. We provide a necessary and sufficient condition for non-injective operators from <i>X</i> to <i>Y</i> to be in the class <span>(mathcal{A}mathcal{M}(X,Y))</span>. We also prove that <i>X</i> is finite dimensional if and only if for every Banach space <i>Y</i>, (<i>X</i>, <i>Y</i>) has the AMp for all minimum norm attaining operators from <i>X</i> to <i>Y</i> if and only if for every Banach space <i>Y</i>, (<i>Y</i>, <i>X</i>) has the AMp for all minimum norm attaining operators from <i>Y</i> to <i>X</i>. We also study the AMp with respect to Crawford number called AMp-<i>c</i> for operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On singular integral operators with reflection 关于带反射的奇异积分算子
IF 0.8
Advances in Operator Theory Pub Date : 2025-01-13 DOI: 10.1007/s43036-024-00416-8
A. G. Kamalyan
{"title":"On singular integral operators with reflection","authors":"A. G. Kamalyan","doi":"10.1007/s43036-024-00416-8","DOIUrl":"10.1007/s43036-024-00416-8","url":null,"abstract":"<div><p>The aim of the present paper is the investigation of matrix singular integral operators with reflection in Lebesgue spaces on the real line with Muckenhoupt weights. It is proved that these operators are matrix coupled with matrix Toeplitz operators. As a corollary, a criterion for the Fredholmness of such operators with piecewise continuous coefficients is obtained. Singular integral operators with flip and Toeplitz plus Hankel operators are also considered.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some weighted norm inequalities for Hilbert C*-modules Hilbert C*模的一些加权范数不等式
IF 0.8
Advances in Operator Theory Pub Date : 2025-01-13 DOI: 10.1007/s43036-024-00418-6
Jing Liu, Deyu Wu, Alatancang Chen
{"title":"Some weighted norm inequalities for Hilbert C*-modules","authors":"Jing Liu,&nbsp;Deyu Wu,&nbsp;Alatancang Chen","doi":"10.1007/s43036-024-00418-6","DOIUrl":"10.1007/s43036-024-00418-6","url":null,"abstract":"<div><p>We present some weighted norm inequalities of bounded adjointable operators on the Hilbert C*-modules. Further, we use the Cartesian decomposition to obtain the lower bounds of numerical radius inequality over Hilbert C*-module. And the existing inequalities of numerical radius on the Hilbert C*-modules are refined.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convergence properties of sequences related to the Ando–Li–Mathias construction and to the weighted Cheap mean 与Ando-Li-Mathias构造和加权廉价均值相关的序列的收敛性
IF 0.8
Advances in Operator Theory Pub Date : 2024-12-28 DOI: 10.1007/s43036-024-00411-z
Dario A. Bini, Bruno Iannazzo, Jie Meng
{"title":"Convergence properties of sequences related to the Ando–Li–Mathias construction and to the weighted Cheap mean","authors":"Dario A. Bini,&nbsp;Bruno Iannazzo,&nbsp;Jie Meng","doi":"10.1007/s43036-024-00411-z","DOIUrl":"10.1007/s43036-024-00411-z","url":null,"abstract":"<div><p>Sequences defining a weighted matrix geometric mean are investigated and their convergence speed is analyzed. The superlinear convergence of a weighted mean based on the Ando–Li–Mathias (ALM) construction is proved. A weighted Cheap mean is defined and conditions on the weights for linear or superlinear convergence of order at least three are provided.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New orthogonality relations based on the norm derivative 基于范数导数的新的正交关系
IF 0.8
Advances in Operator Theory Pub Date : 2024-12-27 DOI: 10.1007/s43036-024-00414-w
Dumitru Popa
{"title":"New orthogonality relations based on the norm derivative","authors":"Dumitru Popa","doi":"10.1007/s43036-024-00414-w","DOIUrl":"10.1007/s43036-024-00414-w","url":null,"abstract":"<div><p>In the paper we introduce new norm derivative mappings and the corresponding orthogonality relations induced by it. We show that this notion is useful in the characterization of inner product spaces, characterization of smooth Banach spaces, Birkhoff orthogonality. We prove also some useful computational formulations.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00414-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Almost Dunford–Pettis p-convergent operators 几乎是Dunford-Pettis p收敛算子
IF 0.8
Advances in Operator Theory Pub Date : 2024-12-27 DOI: 10.1007/s43036-024-00413-x
Halimeh Ardakani, Fateme Vali
{"title":"Almost Dunford–Pettis p-convergent operators","authors":"Halimeh Ardakani,&nbsp;Fateme Vali","doi":"10.1007/s43036-024-00413-x","DOIUrl":"10.1007/s43036-024-00413-x","url":null,"abstract":"<div><p>In this paper two classes of operators related to weakly <i>p</i>-compact and almost Dunford–Pettis sequences which will be called almost Dunford–Pettis <i>p</i>-convergent operators and weak almost <i>p</i>-convergent operators are studied. Some properties of Banach lattices, the weak Dunford–Pettis property of order <i>p</i> and the strong relatively compact Dunford–Pettis property of order <i>p</i> are characterized in terms of almost Dunford–Pettis <i>p</i>-convergent and weak almost <i>p</i>-convergent operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characterization of quasi-parabolic operators and their integral representation 准抛物线算子的特征及其积分表示
IF 0.8
Advances in Operator Theory Pub Date : 2024-12-17 DOI: 10.1007/s43036-024-00409-7
Shubham R. Bais, Pinlodi Mohan, D. Venku Naidu
{"title":"Characterization of quasi-parabolic operators and their integral representation","authors":"Shubham R. Bais,&nbsp;Pinlodi Mohan,&nbsp;D. Venku Naidu","doi":"10.1007/s43036-024-00409-7","DOIUrl":"10.1007/s43036-024-00409-7","url":null,"abstract":"<div><p>The aim of the paper is to characterize all quasi-parabolic operators and provide an integral representation to each quasi-parabolic operator on the Bergman space <span>(A_{lambda }^2(D_n))</span>. We explore some aspects of operator theoretic properties such as compactness, spectrum, common invariant subspaces and more. Further, we show that the collection of all quasi-parabolic operators forms a maximal commutative <span>(C^*)</span>-algebra. As a consequence, we provide integral representation for operators in the <span>(C^*)</span>-algebra generated by Toeplitz operators with essentially bounded quasi-parabolic defining symbols.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On weakly compact multilinear operators and interpolation 弱紧多线性算子与插值
IF 0.8
Advances in Operator Theory Pub Date : 2024-12-12 DOI: 10.1007/s43036-024-00410-0
Antonio Manzano, Mieczysław Mastyło
{"title":"On weakly compact multilinear operators and interpolation","authors":"Antonio Manzano,&nbsp;Mieczysław Mastyło","doi":"10.1007/s43036-024-00410-0","DOIUrl":"10.1007/s43036-024-00410-0","url":null,"abstract":"<div><p>We study weakly compact multilinear operators. We prove a variant of Gantmacher’s weak compactness theorem for multilinear operators. We also present Lions–Peetre type results on weak compactness interpolation for multilinear operators. Furthermore, we provide an analogue of Persson’s result on interpolation of weakly compact operators under the assumption that the target Banach couple satisfies a certain weakly compact approximation property.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00410-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142811104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Banach–Mazur nondensifiability number Banach-Mazur非致密性数
IF 0.8
Advances in Operator Theory Pub Date : 2024-12-09 DOI: 10.1007/s43036-024-00408-8
G. García, G. Mora
{"title":"Banach–Mazur nondensifiability number","authors":"G. García,&nbsp;G. Mora","doi":"10.1007/s43036-024-00408-8","DOIUrl":"10.1007/s43036-024-00408-8","url":null,"abstract":"<div><p>In the present paper, based on the so called degree of nondensifiability (DND), we introduce the concept of Banach–Mazur nondensifiability number of two given Banach spaces and prove that such a number is an optimal lower bound for the well known Banach–Mazur distance. For a given infinite dimensional Banach space, we also introduce a new constant. We demonstrate a relationship between this constant and the Banach–Mazur distance.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142798235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algorithm for spectral factorization of polynomial matrices on the real line 实线上多项式矩阵的谱因式分解算法
IF 0.8
Advances in Operator Theory Pub Date : 2024-11-29 DOI: 10.1007/s43036-024-00406-w
Lasha Ephremidze
{"title":"Algorithm for spectral factorization of polynomial matrices on the real line","authors":"Lasha Ephremidze","doi":"10.1007/s43036-024-00406-w","DOIUrl":"10.1007/s43036-024-00406-w","url":null,"abstract":"<div><p>In this paper, we extend the basic idea of the Janashia–Lagvilava algorithm to adapt it for the spectral factorization of positive-definite polynomial matrices on the real line. This extension results in a new spectral factorization algorithm for polynomial matrix functions defined on <span>(mathbb {R})</span>. The presented numerical example demonstrates that the proposed algorithm outperforms an existing algorithm in terms of accuracy.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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