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Advances in Operator Theory最新文献

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Some special geometric configurations of the eigenvalues of matrices 矩阵特征值的一些特殊几何构型
IF 0.7
Advances in Operator Theory Pub Date : 2026-07-13 DOI: 10.1007/s43036-026-00519-4
Rajesh Sharma, Vijay Sharma
{"title":"Some special geometric configurations of the eigenvalues of matrices","authors":"Rajesh Sharma,&nbsp;Vijay Sharma","doi":"10.1007/s43036-026-00519-4","DOIUrl":"10.1007/s43036-026-00519-4","url":null,"abstract":"<div><p>We obtain some conditions under which all the eigenvalues of a matrix lie at the vertices of a regular polygon. We also consider the case when the eigenvalues lie at the vertices of two concyclic regular polygons. The special cases yield some interesting results about the eigenvalues of unitary matrices and their geometric configurations. Some results related to the similarity of two unitary matrices are also given here.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466012","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
Difference of weighted composition operators from (alpha )-weighted space to radially (omega )-weighted space in the unit ball 单位球中从(alpha ) -加权空间到径向(omega ) -加权空间的加权组合算子的差异
IF 0.7
Advances in Operator Theory Pub Date : 2026-07-09 DOI: 10.1007/s43036-026-00517-6
Cui Chen, Wei Lu, Li Zhang
{"title":"Difference of weighted composition operators from (alpha )-weighted space to radially (omega )-weighted space in the unit ball","authors":"Cui Chen,&nbsp;Wei Lu,&nbsp;Li Zhang","doi":"10.1007/s43036-026-00517-6","DOIUrl":"10.1007/s43036-026-00517-6","url":null,"abstract":"<div><p>In this paper, we study the difference of weighted composition operators acting from the <span>(alpha )</span>-weighted space to radially <span>(omega )</span>-weighted space over the unit ball of <span>(mathbb {C}^m)</span>. We present equivalent characterizations for its boundedness, derive corresponding estimation formulas for its essential norm, and thereby provide equivalent descriptions for its compactness.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465537","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
The polar decomposition of closed linear relations and its applications 封闭线性关系的极坐标分解及其应用
IF 0.7
Advances in Operator Theory Pub Date : 2026-07-09 DOI: 10.1007/s43036-026-00522-9
Mohamed Amine Aouichaoui, Zied Garbouj
{"title":"The polar decomposition of closed linear relations and its applications","authors":"Mohamed Amine Aouichaoui,&nbsp;Zied Garbouj","doi":"10.1007/s43036-026-00522-9","DOIUrl":"10.1007/s43036-026-00522-9","url":null,"abstract":"<div><p>The purpose of this paper is to revisit the polar decomposition theorem for closed everywhere defined linear relations and to illustrate some of its applications. In doing so, we extend Furuta’s results and those of Ito, Yamazaki, and Yanagida, which were previously established for operators, to the realm of closed linear relations. Additionally, we propose potential directions for future research, such as extending the theoretical framework to include <i>C</i>-polar decomposition for closed linear relations, further studying weak-type normal linear relations, and investigating inequalities for closed linear relations components. These developments significantly broaden the scope of polar decomposition theory and open new avenues for further exploration.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465536","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 unbounded complementable operators 关于无界互补算子
IF 0.7
Advances in Operator Theory Pub Date : 2026-06-22 DOI: 10.1007/s43036-026-00516-7
Sachin Manjunath Naik, P. Sam Johnson
{"title":"On unbounded complementable operators","authors":"Sachin Manjunath Naik,&nbsp;P. Sam Johnson","doi":"10.1007/s43036-026-00516-7","DOIUrl":"10.1007/s43036-026-00516-7","url":null,"abstract":"<div><p>The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing complementability in this broader context. The results provide new insights into the structure of unbounded operators, contributing to the ongoing development of operator theory.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-026-00516-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323077","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
Complex symmetric Toeplitz operators through representation theory tools 通过表示理论工具实现复对称Toeplitz算子
IF 0.7
Advances in Operator Theory Pub Date : 2026-06-22 DOI: 10.1007/s43036-026-00518-5
Esteban Heredia-Muñoz, Armando Sánchez-Nungaray, Carlos-Hugo Jiménez-Gómez
{"title":"Complex symmetric Toeplitz operators through representation theory tools","authors":"Esteban Heredia-Muñoz,&nbsp;Armando Sánchez-Nungaray,&nbsp;Carlos-Hugo Jiménez-Gómez","doi":"10.1007/s43036-026-00518-5","DOIUrl":"10.1007/s43036-026-00518-5","url":null,"abstract":"<div><p>Proceeding through a representation theoretic approach, we study the family of Toeplitz operators on the weighted Bergman space <span>(mathcal {H}^2_{alpha }(mathbb {B}_n))</span> whose symbols are invariant under the action of the semidirect group <span>(S_{Delta } rtimes mathbb {T}^{n})</span>, where <span>(S_{Delta })</span> is a subgroup of permutations. Associating a suitable partition <span>(Delta )</span> we associated the conjugation <span>(J_{A})</span> on the Bergman space. Moreover we characterize the complex symmetric Toeplitz operators <span>(T_{a})</span> and <span>(T_{a(r)t^{p}overline{t}^{q}})</span> with respect the conjugation <span>(J_A)</span>, where the symbols are invariant under the action of <span>(S_{Delta } rtimes mathbb {T}^{n})</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-026-00518-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323452","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
Commuting Hankel and Toeplitz operators on the Hardy space of the bidisk 双盘Hardy空间上的交换Hankel算子和Toeplitz算子
IF 0.7
Advances in Operator Theory Pub Date : 2026-06-18 DOI: 10.1007/s43036-026-00513-w
Hong Zou, Tao Yu
{"title":"Commuting Hankel and Toeplitz operators on the Hardy space of the bidisk","authors":"Hong Zou,&nbsp;Tao Yu","doi":"10.1007/s43036-026-00513-w","DOIUrl":"10.1007/s43036-026-00513-w","url":null,"abstract":"<div><p>In this paper, we establish a necessary and sufficient condition for a Toeplitz operator with a bounded pluriharmonic symbol to commute with a Hankel operator with a bounded symbol on the Hardy space of the bidisk.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281123","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
Maps preserving the (partial )-spectrum of skew products of operators 保留算子的偏积(partial ) -谱的映射
IF 0.7
Advances in Operator Theory Pub Date : 2026-06-15 DOI: 10.1007/s43036-026-00515-8
Hassane Benbouziane, Aukacha Daoudi, Mustapha Ech-Chérif El Kettani, Ismail El Khchin
{"title":"Maps preserving the (partial )-spectrum of skew products of operators","authors":"Hassane Benbouziane,&nbsp;Aukacha Daoudi,&nbsp;Mustapha Ech-Chérif El Kettani,&nbsp;Ismail El Khchin","doi":"10.1007/s43036-026-00515-8","DOIUrl":"10.1007/s43036-026-00515-8","url":null,"abstract":"<div><p>Let <span>(mathcal {B}(mathcal {H}))</span> be the algebra of all bounded linear operators on an infinite-dimensional Hilbert space <span>(mathcal {H})</span>. A map <span>(Delta )</span>, from <span>( mathcal {B}(mathcal {H}) )</span> into a closed subset of <span>( mathbb {C} )</span> is said to be a <span>(partial )</span>-spectrum if <span>(partial sigma (T) subseteq Delta (T) subseteq sigma (T))</span> for all <span>(T in mathcal {B}(mathcal {H}))</span>, where <span>(sigma (T))</span> denotes the spectrum of <i>T</i> and <span>(partial sigma (T))</span> its boundary. Fix a <span>(partial )</span>-spectrum map <span>(Delta )</span>. In this paper, we characterize all maps <span>(phi :mathcal {B}(mathcal {H}) rightarrow mathcal {B}(mathcal {H}))</span> whose ranges contain all operators of rank at most two and that satisfy either <span>(Delta (TS^*) = Delta big (phi (T)phi (S)^*big ))</span> for all <span>(T,S in mathcal {B}(mathcal {H}))</span> or <span>(Delta (TS^*T) = Delta big (phi (T)phi (S)^*phi (T)big ))</span> for all <span>(T,S in mathcal {B}(mathcal {H}).)</span></p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281017","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 the conjugate weight function and ultradifferentiable classes of entire functions 共轭权函数与整个函数的超可微类。
IF 0.7
Advances in Operator Theory Pub Date : 2026-06-15 DOI: 10.1007/s43036-026-00503-y
Gerhard Schindl
{"title":"On the conjugate weight function and ultradifferentiable classes of entire functions","authors":"Gerhard Schindl","doi":"10.1007/s43036-026-00503-y","DOIUrl":"10.1007/s43036-026-00503-y","url":null,"abstract":"<div><p>We introduce the new notion of a conjugate weight function and provide a detailed study of this operation and its properties. Then we apply this knowledge to study classes of ultradifferentiable functions defined in terms of fast growing weight functions in the sense of Braun–Meise–Taylor and hence violating standard regularity requirements. Therefore, we transfer recent results shown by the author and D.N. Nenning from the weight sequence to the weight function framework. In order to proceed and to complete the picture we also define the conjugate associated weight matrix and investigate the relation to conjugate weight sequences via the corresponding associate weight functions. Finally, as it has already been done in the weight sequence case, we generalize results by M. Markin from the small Gevrey-setting and show how the corresponding non-standard ultradifferentiable function classes can be used to detect boundedness of normal linear operators on Hilbert spaces (associated with an evolution equation problem). On the one hand, when involving the weight matrix here the crucial information concerning regularity of the weak solutions can be expressed in terms of only one weight, namely of the given weight function. But, on the other hand, for the connection to the weighted entire setting the required conditions on the weight function are too restrictive in the general case.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13269427/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148273325","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
A characterization of amenability property of WAP(S) in locally convex spaces 局部凸空间中WAP(S)的适应性表征
IF 0.7
Advances in Operator Theory Pub Date : 2026-06-08 DOI: 10.1007/s43036-026-00507-8
Khadime Salame
{"title":"A characterization of amenability property of WAP(S) in locally convex spaces","authors":"Khadime Salame","doi":"10.1007/s43036-026-00507-8","DOIUrl":"10.1007/s43036-026-00507-8","url":null,"abstract":"<div><p>This paper is a sequel of a recent work regarding an open problem posted by Lau and Zhang on a characterization of existence of a left invariant mean on WAP(<i>S</i>), the Banach algebra of weakly almost periodic functions of a semitopological semigroup <i>S</i>, in terms of a fixed point property for nonexpnsive mappings on weakly compact convex sets in locally convex spaces. More precisely, it is about whether (left) amenability of WAP(<i>S</i>) of a given semitopological semigroup <i>S</i> is equivalent to the following fixed point property: (<b>F</b>): Every weakly separately continuous, weakly quasi-equicontinuous and <i>Q</i>-nonexpansive action of <i>S</i> on a weakly compact convex set K in a separated locally convex topological vector space (<i>E</i>, <i>Q</i>) has a common fixed point for <i>S</i>. In this paper, we provide a complete answer to this question for arbitrary semitopological semigroups.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148236831","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
Grothendieck–Pietsch composition results for multiple summing operators 多个求和算子的Grothendieck-Pietsch组合结果
IF 0.7
Advances in Operator Theory Pub Date : 2026-06-03 DOI: 10.1007/s43036-026-00511-y
Dumitru Popa
{"title":"Grothendieck–Pietsch composition results for multiple summing operators","authors":"Dumitru Popa","doi":"10.1007/s43036-026-00511-y","DOIUrl":"10.1007/s43036-026-00511-y","url":null,"abstract":"<div><p>We prove Grothendieck–Pietsch composition results for multiple summing operators without a linear analogue. As application, we give a new proof for the multilinear version of Grothendieck’s composition theorem proven by D. P érez-García and I. Villanueva. We use this result in tandem with the Maurey factorization theorem, to find the necessary and sufficient conditions for multilinear multiplication operator from a product of <span>(l_{p})</span> spaces into <span>(l_{1})</span> to be multiple 2-summing.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-026-00511-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172625","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
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