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Birkhoff-James orthogonality in certain tensor products of Banach spaces Banach空间某些张量积中的Birkhoff-James正交性
IF 0.5 4区 数学
Operators and Matrices Pub Date : 2022-10-25 DOI: 10.7153/oam-2023-17-17
Mohit, R. Jain
{"title":"Birkhoff-James orthogonality in certain tensor products of Banach spaces","authors":"Mohit, R. Jain","doi":"10.7153/oam-2023-17-17","DOIUrl":"https://doi.org/10.7153/oam-2023-17-17","url":null,"abstract":"In this article, the relationship between Birkhoff-James orthogonality of elementary tensors in certain tensor product spaces with the Birkhoff-James orthogonality of individual elements in their respective spaces is studied.","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45863838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Weak expectations of discrete quantum group algebras and crossed products 离散量子群代数与叉积的弱期望
IF 0.5 4区 数学
Operators and Matrices Pub Date : 2022-08-30 DOI: 10.7153/oam-2023-17-06
A. Bhattacharjee, Angshuman Bhattacharya
{"title":"Weak expectations of discrete quantum group algebras and crossed products","authors":"A. Bhattacharjee, Angshuman Bhattacharya","doi":"10.7153/oam-2023-17-06","DOIUrl":"https://doi.org/10.7153/oam-2023-17-06","url":null,"abstract":"In this article we study analogues of the weak expectation property of discrete group C*-algebras and their crossed products, in the discrete quantum group setting, i.e., discrete quantum group C*-algebras and crossed products of C*-algebras with amenable discrete quantum groups.","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41361835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Bidiagonal decompositions and total positivity of some special matrices 一些特殊矩阵的双对角分解和全正性
IF 0.5 4区 数学
Operators and Matrices Pub Date : 2022-05-29 DOI: 10.7153/oam-2022-16-41
Priyanka Grover, Veer Singh Panwar
{"title":"Bidiagonal decompositions and total positivity of some special matrices","authors":"Priyanka Grover, Veer Singh Panwar","doi":"10.7153/oam-2022-16-41","DOIUrl":"https://doi.org/10.7153/oam-2022-16-41","url":null,"abstract":"The matrix S = [1 + x i y j ] ni,j =1 , 0 < x 1 < · · · < x n , 0 < y 1 < · · · < y n , has gained importance lately due to its role in powers preserving total nonnegativity. We give an explicit decomposition of S in terms of elementary bidiagonal matrices, which is analogous to the Neville decomposition . We give a bidiagonal decomposition of S ◦ m = [(1 + x i y j ) m ] for positive integers 1 ≤ m ≤ n − 1. We also explore the total positivity of Hadamard powers of another important class of matrices called mean matrices .","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49148398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 matrix Cauchy-Schwarz inequality 关于矩阵Cauchy-Schwarz不等式
IF 0.5 4区 数学
Operators and Matrices Pub Date : 2022-05-05 DOI: 10.7153/oam-2023-17-34
M. Sababheh, C. Conde, H. Moradi
{"title":"On the matrix Cauchy-Schwarz inequality","authors":"M. Sababheh, C. Conde, H. Moradi","doi":"10.7153/oam-2023-17-34","DOIUrl":"https://doi.org/10.7153/oam-2023-17-34","url":null,"abstract":"The main goal of this work is to present new matrix inequalities of the Cauchy-Schwarz type. In particular, we investigate the so-called Lieb functions, whose definition came as an umbrella of Cauchy-Schwarz-like inequalities, then we consider the mixed Cauchy-Schwarz inequality. This latter inequality has been influential in obtaining several other matrix inequalities, including numerical radius and norm results. Among many other results, we show that [left| T right|le frac{1}{4}left( left| left| T right|+left| {{T}^{*}} right|+2mathfrak RT right|+left| left| T right|+left| {{T}^{*}} right|-2mathfrak RT right| right),] where $mathfrak RT$ is the real part of $T$.","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42475478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Powers of posinormal operators 伪正规算子的幂
IF 0.5 4区 数学
Operators and Matrices Pub Date : 2022-02-19 DOI: 10.7153/OAM-10-02
C. Kubrusly, P. Vieira, J. Zanni
{"title":"Powers of posinormal operators","authors":"C. Kubrusly, P. Vieira, J. Zanni","doi":"10.7153/OAM-10-02","DOIUrl":"https://doi.org/10.7153/OAM-10-02","url":null,"abstract":"Square of a posinormal operator is not necessarily posinormal. But (i) powers of quasiposinormal operators are quasiposinormal and, under closed ranges assumption, powers of (ii) posinormal operators are posinormal, (iii) of operators that are both posinormal and coposinormal are posinormal and coposinormal, and (iv) of semi-Fredholm posinormal operators are posinormal.","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":"1 1","pages":"15-27"},"PeriodicalIF":0.5,"publicationDate":"2022-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43064827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 10
On some algebraic properties of block Toeplitz matrices with commuting entries 具有交换项的块Toeplitz矩阵的一些代数性质
IF 0.5 4区 数学
Operators and Matrices Pub Date : 2022-01-29 DOI: 10.7153/oam-2022-16-61
M. A. Khan, A. Yagoub
{"title":"On some algebraic properties of block Toeplitz matrices with commuting entries","authors":"M. A. Khan, A. Yagoub","doi":"10.7153/oam-2022-16-61","DOIUrl":"https://doi.org/10.7153/oam-2022-16-61","url":null,"abstract":". Toeplitz matrices are ubiquitous and play important roles across many areas of mathematics. In this paper, we present some algebraic results concerning block Toeplitz matrices with block entries belonging to a commutative algebra A . The characterization of normal block Toeplitz matrices with entries from A is also obtained.","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46777201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Restricted invertibility of continuous matrix functions 连续矩阵函数的有限可逆性
IF 0.5 4区 数学
Operators and Matrices Pub Date : 2022-01-11 DOI: 10.7153/oam-2022-16-78
Adrian Fan, Jack Montemurro, P. Motakis, Naina Praveen, A. Rusonik, P. Skoufranis, N. Tobin
{"title":"Restricted invertibility of continuous matrix functions","authors":"Adrian Fan, Jack Montemurro, P. Motakis, Naina Praveen, A. Rusonik, P. Skoufranis, N. Tobin","doi":"10.7153/oam-2022-16-78","DOIUrl":"https://doi.org/10.7153/oam-2022-16-78","url":null,"abstract":"Motivated by an influential result of Bourgain and Tzafriri, we consider continuous matrix functions $A:mathbb{R}to M_{ntimes n}$ and lower $ell_2$-norm bounds associated with their restriction to certain subspaces. We prove that for any such $A$ with unit-length columns, there exists a continuous choice of subspaces $tmapsto U(t)subset mathbb{R}^n$ such that for $vin U(t)$, $|A(t)v|geq c|v|$ where $c$ is some universal constant. Furthermore, the $U(t)$ are chosen so that their dimension satisfies a lower bound with optimal asymptotic dependence on $n$ and $sup_{tin mathbb{R}}|A(t)|.$ We provide two methods. The first relies on an orthogonality argument, while the second is probabilistic and combinatorial in nature. The latter does not yield the optimal bound for $dim(U(t))$ but the $U(t)$ obtained in this way are guaranteed to have a canonical representation as joined-together spaces spanned by subsets of the unit vector basis.","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46745343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Solution algorithm of the inverse spectral problem for Dirac operator with a spectral parameter in the boundary condition 边界条件下带谱参数的Dirac算子谱反问题的求解算法
IF 0.5 4区 数学
Operators and Matrices Pub Date : 2022-01-01 DOI: 10.7153/oam-2022-16-11
Abid G. Ferzullazadeh
{"title":"Solution algorithm of the inverse spectral problem for Dirac operator with a spectral parameter in the boundary condition","authors":"Abid G. Ferzullazadeh","doi":"10.7153/oam-2022-16-11","DOIUrl":"https://doi.org/10.7153/oam-2022-16-11","url":null,"abstract":". We consider an inverse problem for Dirac system in case where one of nonseparated boundary conditions involves a linear function of spectral parameter. We prove the uniqueness theorem for the solution of this problem and then, based on this theorem, we construct a solution algorithm for the considered problem.","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71222856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Determinantal polynomials of a weighted shift matrix with palindromic geometric weights 具有回文几何权值的加权移位矩阵的行列式多项式
IF 0.5 4区 数学
Operators and Matrices Pub Date : 2022-01-01 DOI: 10.7153/oam-2022-16-24
Undrakh Batzorig
{"title":"Determinantal polynomials of a weighted shift matrix with palindromic geometric weights","authors":"Undrakh Batzorig","doi":"10.7153/oam-2022-16-24","DOIUrl":"https://doi.org/10.7153/oam-2022-16-24","url":null,"abstract":"","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71222973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2
Generalizing the Ando-Hiai inequality for sectorial matrices 对扇形矩阵的Ando-Hiai不等式的推广
IF 0.5 4区 数学
Operators and Matrices Pub Date : 2022-01-01 DOI: 10.7153/oam-2022-16-26
Linlong Zhao, Yanp ng Zheng, Xia yu Jiang
{"title":"Generalizing the Ando-Hiai inequality for sectorial matrices","authors":"Linlong Zhao, Yanp ng Zheng, Xia yu Jiang","doi":"10.7153/oam-2022-16-26","DOIUrl":"https://doi.org/10.7153/oam-2022-16-26","url":null,"abstract":"","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71223031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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