Singular value inequalities for commutators of Hilbert space operators

被引：8
|
作者：
Kittaneh, Fuad [1 ]
机构：
[1] Univ Jordan, Dept Math, Amman, Jordan
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2009年 / 430卷 / 8-9期
关键词：
Singular value; Commutator; Compact operator; Positive operator; Self-adjoint operator; Normal operator; Unitarily invariant norm; Inequality; SELF-ADJOINT OPERATORS; POSITIVE OPERATORS; WENZELS CONJECTURE; NORM INEQUALITIES; MATRICES; BOTTCHER; PROOF;
D O I：
10.1016/j.laa.2008.12.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove several singular value inequalities for commutators of Hilbert space operators. It is shown, among other inequalities, that if A, B, and X are operators on a complex separable Hilbert space such that A and B are positive, and X is compact, then the singular values of AX - XB are dominated by those of max(parallel to A parallel to, parallel to B parallel to)(X circle plus X) where parallel to (.) parallel to is the usual operator norm. (C) 2008 Elsevier Inc. All rights reserved.
引用
收藏
页码：2362 / 2367
页数：6
相关论文
共 50 条
  • [1] Singular Value inequalities for Hilbert space Operators
    Alfakhr, Mahdi Taleb
    Omidvar, Mohsen Erfanian
    FILOMAT, 2018, 32 (08) : 2861 - 2866
  • [2] Numerical Radius Inequalities for Commutators of Hilbert Space Operators
    Hirzallah, Omar
    Kittaneh, Fuad
    Shebrawi, Khalid
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2011, 32 (07) : 739 - 749
  • [3] SOME RESULTS ON SINGULAR VALUE INEQUALITIES OF COMPACT OPERATORS IN HILBERT SPACE
    Taghavi, A.
    Darvish, V.
    Nazari, H. M.
    Dragomir, S. S.
    MATHEMATICAL REPORTS, 2016, 18 (04): : 545 - 555
  • [4] Some singular value and unitarily invariant norm inequalities for Hilbert space operators
    Taghavi A.
    Darvish V.
    Nazari H.M.
    Dragomir S.S.
    ANNALI DELL'UNIVERSITA' DI FERRARA, 2017, 63 (2) : 377 - 389
  • [5] COMMUTATORS OF OPERATORS ON HILBERT SPACE
    BROWN, A
    HALMOS, PR
    PEARCY, C
    CANADIAN JOURNAL OF MATHEMATICS, 1965, 17 (05): : 695 - &
  • [6] ON COMMUTATORS OF OPERATORS ON HILBERT SPACE
    PEARCY, C
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 16 (01) : 53 - &
  • [7] Norm inequalities for the absolute value of Hilbert space operators
    Shebrawi, Khalid
    Albadawi, Hussien
    LINEAR & MULTILINEAR ALGEBRA, 2010, 58 (04): : 453 - 463
  • [8] Some singular value inequalities on commutators
    Kaur, Maninderjit
    Garg, Isha
    ADVANCES IN OPERATOR THEORY, 2025, 10 (01)
  • [9] SOME INEQUALITIES FOR COMMUTATORS OF BOUNDED LINEAR OPERATORS IN HILBERT SPACES
    Dragomir, S. S.
    FILOMAT, 2011, 25 (02) : 151 - 162
  • [10] On commutators of square-zero Hilbert space operators
    Marcoux, Laurent W.
    Radjavi, Heydar
    Zhang, Yuanhang
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2025,
12345