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Advances in Operator Theory最新文献

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Structure and applications of n-quasi exponentially m-isometric operators n-拟指数m-等距算子的结构与应用
IF 0.8
Advances in Operator Theory Pub Date : 2025-05-26 DOI: 10.1007/s43036-025-00445-x
Abeer A. Al Dohiman, Mohamed Amine Aouichaoui, Sid Ahmed Ould Ahmed Mahmoud
{"title":"Structure and applications of n-quasi exponentially m-isometric operators","authors":"Abeer A. Al Dohiman,&nbsp;Mohamed Amine Aouichaoui,&nbsp;Sid Ahmed Ould Ahmed Mahmoud","doi":"10.1007/s43036-025-00445-x","DOIUrl":"10.1007/s43036-025-00445-x","url":null,"abstract":"<div><p>In this paper, we aim to extend the established theory of exponentially <i>m</i>-isometric operators by introducing and exploring the concept of <i>n</i>-quasi-exponentially m-isometric operators. This generalization allows us to investigate a broader class of operators. We provide a comprehensive analysis of various key properties of these operators, which are illustrated through specific matrix representations. An examination of their spectral properties is also provided. The open questions presented at the end pave the way for further research and the continued advancement of the theory of <i>m</i>-isometries and related operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140233","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
Extension of m-isometric weighted composition operators on directed graphs 有向图上m等距加权复合算子的推广
IF 0.8
Advances in Operator Theory Pub Date : 2025-05-23 DOI: 10.1007/s43036-025-00447-9
V. Devadas, E. Shine Lal, T. Prasad
{"title":"Extension of m-isometric weighted composition operators on directed graphs","authors":"V. Devadas,&nbsp;E. Shine Lal,&nbsp;T. Prasad","doi":"10.1007/s43036-025-00447-9","DOIUrl":"10.1007/s43036-025-00447-9","url":null,"abstract":"<div><p>In this paper, we discuss <i>k</i>-quasi-<i>m</i>-isometric composition operators and weighted composition operators on directed graphs with one circuit and more than one branching vertex.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117625","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
Regular traces on ideals in (mathcal {L}(H)) 规律的痕迹就在理想之中 (mathcal {L}(H))
IF 0.8
Advances in Operator Theory Pub Date : 2025-05-16 DOI: 10.1007/s43036-025-00446-w
F. Sukochev, D. Zanin
{"title":"Regular traces on ideals in (mathcal {L}(H))","authors":"F. Sukochev,&nbsp;D. Zanin","doi":"10.1007/s43036-025-00446-w","DOIUrl":"10.1007/s43036-025-00446-w","url":null,"abstract":"<div><p>On a Banach ideal the set of continuous traces is spanned by the set of positive traces. We extend this result by showing that on an arbitrary ideal the set of all regular traces is the linear span of the set of positive traces.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073621","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
Power-regularity of weighted shift operators
IF 0.8
Advances in Operator Theory Pub Date : 2025-05-13 DOI: 10.1007/s43036-025-00442-0
Chaolong Hu, Youqing Ji
{"title":"Power-regularity of weighted shift operators","authors":"Chaolong Hu,&nbsp;Youqing Ji","doi":"10.1007/s43036-025-00442-0","DOIUrl":"10.1007/s43036-025-00442-0","url":null,"abstract":"<div><p>A linear bounded operator <i>T</i> on a complex Banach space <i>X</i> is said to be <i>power-regular</i> if the sequence <span>({Vert T^n xVert ^{frac{1}{n}}}_{n=1}^{infty })</span> is convergent for every <span>(xin X)</span>. For unilateral weighted shift <i>S</i>, we give a sufficient condition that <i>S</i> is power-regular. As an application, we construct a class of power-regular operators. Moreover, we show that there exist invertible power-regular bilateral weighted shifts, whose inverses are not power-regular.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944180","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
Spectral decomposition of power-bounded operators: the finite spectrum case 幂有界算子的谱分解：有限谱情况
IF 0.8
Advances in Operator Theory Pub Date : 2025-05-12 DOI: 10.1007/s43036-025-00441-1
Shiho Oi, Jyamira Oppekepenguin
{"title":"Spectral decomposition of power-bounded operators: the finite spectrum case","authors":"Shiho Oi,&nbsp;Jyamira Oppekepenguin","doi":"10.1007/s43036-025-00441-1","DOIUrl":"10.1007/s43036-025-00441-1","url":null,"abstract":"<div><p>In this paper, we investigate power-bounded operators, including surjective isometries, on Banach spaces. Koehler and Rosenthal asserted that an isolated point in the spectrum of a surjective isometry on a Banach space lies in the point spectrum, with the corresponding eigenspace having an invariant complement. However, they did not provide a detailed proof of this claim, at least as understood by the authors of this manuscript. Here, by applications of a theorem of Gelfand and the Riesz projections, we demonstrate that the theorem of Koehler and Rosenthal holds for any power-bounded operator on a Banach space. This not only furnishes a detailed proof of the theorem but also slightly generalizes its scope. As a result, we establish that if <span>(T: X rightarrow X)</span> is a power-bounded operator on a Banach space <i>X</i> whose spectrum consists of finitely many points <span>({lambda _1, lambda _2, dots , lambda _m})</span>, then for every <span>(1 le i, j le m)</span>, there exist projections <span>(P_j)</span> on <i>X</i> such that <span>(P_iP_j=delta _{ij}P_i)</span>, <span>(sum _{j=1}^mP_j=I)</span>, and <span>(T=Sigma _{j=1}^m lambda _j P_j)</span>. It follows that such an operator <i>T</i> is an algebraic operator.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143938524","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
Expansion of traces and Dixmier traceability for global pseudo-differential operators on manifolds with boundary 具有边界流形上全局伪微分算子的迹展开和Dixmier可追溯性
IF 0.8
Advances in Operator Theory Pub Date : 2025-05-09 DOI: 10.1007/s43036-025-00438-w
Duván Cardona, Vishvesh Kumar, Michael Ruzhansky, Niyaz Tokmagambetov
{"title":"Expansion of traces and Dixmier traceability for global pseudo-differential operators on manifolds with boundary","authors":"Duván Cardona,&nbsp;Vishvesh Kumar,&nbsp;Michael Ruzhansky,&nbsp;Niyaz Tokmagambetov","doi":"10.1007/s43036-025-00438-w","DOIUrl":"10.1007/s43036-025-00438-w","url":null,"abstract":"<div><p>Given a smooth manifold <i>M</i> (with or without boundary), in this paper we study the regularisation of traces for the global pseudo-differential calculus in the context of non-harmonic analysis. Indeed, using the global pseudo-differential calculus on manifolds (with or without boundary) developed in Ruzhansky and Tokmagambetov (Int Math Res Not IMRN 12:3548–3615, 2016), the Calderón–Vaillancourt Theorem and the global functional calculus in Cardona et al. (Adv Oper Theory arXiv:2101.02519, 2020), we determine the singularity orders in the regularisation of traces and the sharp regularity orders for the Dixmier traceability of the global Hörmander classes. Our analysis (free of coordinate systems) allows us to obtain non-harmonic analogues of several classical results arising from the microlocal analysis of regularised traces for pseudo-differential operators with symbols defined by localisations.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00438-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925646","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
On the spectrum of supercyclic/hypercyclic operators 关于超环/超环算子的谱
IF 0.8
Advances in Operator Theory Pub Date : 2025-04-30 DOI: 10.1007/s43036-025-00437-x
Pietro Aiena, Fabio Burderi, Salvatore Triolo
{"title":"On the spectrum of supercyclic/hypercyclic operators","authors":"Pietro Aiena,&nbsp;Fabio Burderi,&nbsp;Salvatore Triolo","doi":"10.1007/s43036-025-00437-x","DOIUrl":"10.1007/s43036-025-00437-x","url":null,"abstract":"<div><p>This paper concerns the spectral structure of hypercyclic and supercyclic operators defined on Banach spaces, or defined on Hilbert spaces. We also consider the spectral properties of operators in Hilbert spaces that commute with a hypercyclic operator. A result of Herrero and Kitai (Proc Am Math Soc 116(3):873–875, 1992) is extended to Drazin invertible operators. In particular, a Drazin invertible operator is hypercyclic if and only if is invertible. An analogous result holds for supercyclic operators <i>T</i> in the case were the dual <span>(T^*)</span> has empty point spectrum.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00437-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143888643","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
On dynamics of quantum states generated by averaging of random shifts 随机位移平均产生的量子态动力学
IF 0.8
Advances in Operator Theory Pub Date : 2025-04-25 DOI: 10.1007/s43036-025-00440-2
Grigori Amosov, Vsevolod Sakbaev
{"title":"On dynamics of quantum states generated by averaging of random shifts","authors":"Grigori Amosov,&nbsp;Vsevolod Sakbaev","doi":"10.1007/s43036-025-00440-2","DOIUrl":"10.1007/s43036-025-00440-2","url":null,"abstract":"<div><p>Quantum channels are usually studied as the completely positive trace preserving linear mapping of the space of normal quantum states into itself. We study the extension of an above quantum channel to the space of quantum states of general type that are convex combinations of normal states and singular states according to the Yosida–Hewitt decomposition. The interest to the study of quantum dynamics on the set of general quantum states arises in the consideration of a quantum dynamical semigroup acting in a Hilbert space of functions of infinite dimensional argument. In this case the above semigroup maps any pure vector quantum state into a state of general type. This effect can be considered in the example of averaging of quantum dynamical semigroup generated by a shift argument on a random Gaussian vector.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875465","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 the existence of an (L)-(U) factorization 表征一个(L) - (U)分解的存在性
IF 0.8
Advances in Operator Theory Pub Date : 2025-04-16 DOI: 10.1007/s43036-024-00400-2
Charles R. Johnson, Pavel Okunev
{"title":"Characterization of the existence of an (L)-(U) factorization","authors":"Charles R. Johnson,&nbsp;Pavel Okunev","doi":"10.1007/s43036-024-00400-2","DOIUrl":"10.1007/s43036-024-00400-2","url":null,"abstract":"<div><p>For the first time, a characterization is given of the circumstances under which an <i>n</i>-by-<i>n</i> matrix over a field has an <span>(L)</span>-<span>(U)</span> factorization. This is in terms of a comparison of ranks of the leading <i>k</i>-by-<i>k</i> principal submatrix to the rank of the first <i>k</i> columns and first <i>k</i> rows. Known results about special types of <span>(L)</span>-<span>(U)</span> factorizations follow as do some new results about near <span>(L)</span>-<span>(U)</span> factorization when a conventional <span>(L)</span>-<span>(U)</span> factorization does not exist. The proof allows explicit construction of an <span>(L)</span>-<span>(U)</span> factorization when one exists.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143840488","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
Sampling recovery of functions with mixed smoothness 混合平滑函数的采样恢复
IF 0.8
Advances in Operator Theory Pub Date : 2025-04-12 DOI: 10.1007/s43036-025-00439-9
E. D. Kosov, V. N. Temlyakov
{"title":"Sampling recovery of functions with mixed smoothness","authors":"E. D. Kosov,&nbsp;V. N. Temlyakov","doi":"10.1007/s43036-025-00439-9","DOIUrl":"10.1007/s43036-025-00439-9","url":null,"abstract":"<div><p>Recently, a substantial progress in studying the problem of optimal sampling recovery was made in a number of papers. In particular, this resulted in some progress in studying sampling recovery on function classes with mixed smoothness. Mostly, the case of recovery in the square norm was studied. In this paper we combine some of the new ideas developed recently in order to obtain progress in sampling recovery on classes with mixed smoothness in other integral norms.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143824588","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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