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Advances in Operator Theory最新文献

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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
Little Hankel operators from Bloch type spaces into another 小汉克尔算子从布洛赫输入空间到另一个
IF 0.8
Advances in Operator Theory Pub Date : 2024-11-29 DOI: 10.1007/s43036-024-00405-x
Kiyoki Tanaka, Satoshi Yamaji
{"title":"Little Hankel operators from Bloch type spaces into another","authors":"Kiyoki Tanaka,&nbsp;Satoshi Yamaji","doi":"10.1007/s43036-024-00405-x","DOIUrl":"10.1007/s43036-024-00405-x","url":null,"abstract":"<div><p>A characterization for the boundedness of multiplication and composition operators on Bloch type spaces is well-known. Wu, Zhao and Zorboska gave necessary and sufficient conditions for Toeplitz operators on Bloch type spaces to be bounded. In this paper, we discuss the boundedness of little Hankel operators with anti holomorphic symbols from a Bloch type space to an another Bloch type space.</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":"142754346","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
Stability in non-normal periodic Jacobi operators: advancing Börg’s theorem 非正态周期雅可比算子的稳定性：推进伯格定理
IF 0.8
Advances in Operator Theory Pub Date : 2024-11-28 DOI: 10.1007/s43036-024-00402-0
G. Krishna Kumar, V. B. Kiran Kumar
{"title":"Stability in non-normal periodic Jacobi operators: advancing Börg’s theorem","authors":"G. Krishna Kumar,&nbsp;V. B. Kiran Kumar","doi":"10.1007/s43036-024-00402-0","DOIUrl":"10.1007/s43036-024-00402-0","url":null,"abstract":"<div><p>Periodic Jacobi operators naturally arise in numerous applications, forming a cornerstone in various fields. The spectral theory associated with these operators boasts an extensive body of literature. Considered as discretized counterparts of Schrödinger operators, widely employed in quantum mechanics, Jacobi operators play a crucial role in mathematical formulations. The classical uniqueness result by G. Börg in 1946 occupies a significant place in the literature of inverse spectral theory and its applications. This result is closely intertwined with M. Kac’s renowned article, ‘Can one hear the shape of a drum?’ published in 1966. Since 1975,  discrete versions of Börg’s theorem have been available in the literature. In this article, we concentrate on the non-normal periodic Jacobi operator and the discrete versions of Börg’s Theorem. We extend recently obtained stability results to cover non-normal cases. The existing stability findings establish a correlation between the oscillations of the matrix entries and the size of the spectral gap. Our result covers the current self-adjoint versions of Börg’s theorem, including recent quantitative variations. Here, the oscillations of the matrix entries are linked to the path-connectedness of the pseudospectrum. Additionally, we explore finite difference approximations of various linear differential equations as specific applications.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142736900","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 maximal hyperplane sections of the unit ball of (l_p^n) for (p>2) 关于（p>2）的（l_p^n）单位球的最大超平面部分
IF 0.8
Advances in Operator Theory Pub Date : 2024-11-21 DOI: 10.1007/s43036-024-00404-y
Hermann König
{"title":"On maximal hyperplane sections of the unit ball of (l_p^n) for (p>2)","authors":"Hermann König","doi":"10.1007/s43036-024-00404-y","DOIUrl":"10.1007/s43036-024-00404-y","url":null,"abstract":"<div><p>The maximal hyperplane section of the <span>(l_infty ^n)</span>-ball, i.e. of the <i>n</i>-cube, is the one perpendicular to <span>(frac{1}{sqrt{2}} (1,1,0 ,ldots ,0))</span>, as shown by Ball. Eskenazis, Nayar and Tkocz extended this result to the <span>(l_p^n)</span>-balls for very large <span>(p ge 10^{15})</span>. By Oleszkiewicz, Ball’s result does not transfer to <span>(l_p^n)</span> for <span>(2&lt; p &lt; p_0 simeq 26.265)</span>. Then the hyperplane section perpendicular to the main diagonal yields a counterexample for large dimensions <i>n</i>. Suppose that <span>(p_0 le p &lt; infty )</span>. We show that the analogue of Ball’s result holds in <span>(l_p^n)</span>-balls for all hyperplanes with normal unit vectors <i>a</i>, if all coordinates of <i>a</i> have modulus <span>(le frac{1}{sqrt{2}})</span> and <i>p</i> has distance <span>(ge 2^{-p})</span> to the even integers. Under similar assumptions, we give a Gaussian upper bound for <span>(20&lt; p &lt; p_0)</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00404-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679823","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
Commutativity and spectral properties for a general class of Szász–Mirakjan–Durrmeyer operators 一般类 Szász-Mirakjan-Durrmeyer 算子的交换性和谱特性
IF 0.8
Advances in Operator Theory Pub Date : 2024-11-21 DOI: 10.1007/s43036-024-00403-z
Ulrich Abel, Ana Maria Acu, Margareta Heilmann, Ioan Raşa
{"title":"Commutativity and spectral properties for a general class of Szász–Mirakjan–Durrmeyer operators","authors":"Ulrich Abel,&nbsp;Ana Maria Acu,&nbsp;Margareta Heilmann,&nbsp;Ioan Raşa","doi":"10.1007/s43036-024-00403-z","DOIUrl":"10.1007/s43036-024-00403-z","url":null,"abstract":"<div><p>In this paper we present commutativity results for a general class of Szász–Mirakjan–Durrmeyer type operators and associated differential operators and investigate their eigenfunctions.Please confirm if the inserted city names are correct. Amend if necessary.The inserted city name is correct.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00403-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679819","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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