Vector norm inequalities for power series of operators in Hilbert spaces

被引：2
|
作者：
Chenung, W. S. [1 ]
Dragomir, S. S. [2 ,3 ]
机构：
[1] Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China
[2] Victoria Univ, Sch Engn & Sci, Math, Melbourne, Vic 8001, Australia
[3] Univ Witwatersrand, Sch Computat & Applied Math, ZA-2050 Johannesburg, South Africa
来源：
TBILISI MATHEMATICAL JOURNAL | 2014年 / 7卷 / 02期
关键词：
Bounded linear operators; Hilbert spaces; Functions of operators; Power series; Hermite-Hadamard type inequalities;
D O I：
10.2478/tmj-2014-0013
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, vector norm inequalities that provides upper bounds for the Lipschitz quantity parallel to f (T) x - f (V) x parallel to for power series f(z) = Sigma(infinity)(n=0) a(n)z(n), bounded linear operators T,V on the Hilbert space H and vectors x epsilon H are established. Applications in relation to Hermite-Hadamard type inequalities and examples for elementary functions of interest are given as well.
引用
收藏
页码：21 / 34
页数：14
相关论文
共 50 条
  • [31] Some Vector Inequalities for Continuous Functions of Self-Adjoint Operators in Hilbert Spaces
    Dragomir, S. S.
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2011,
  • [32] VECTOR SEMINORMS, SPACES WITH VECTOR NORM, AND REGULAR OPERATORS
    Cristescu, Romulus
    REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES, 2008, 53 (5-6): : 407 - 418
  • [33] NORM CONVERGENCE OF SECTORIAL OPERATORS ON VARYING HILBERT SPACES
    Mugnolo, Delio
    Nittka, Robin
    Post, Olaf
    OPERATORS AND MATRICES, 2013, 7 (04): : 955 - 995
  • [34] SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS
    Hasankhani, A.
    Nazari, A.
    Saheli, M.
    IRANIAN JOURNAL OF FUZZY SYSTEMS, 2010, 7 (03): : 129 - 157
  • [35] Twice Differentiable Ostrowski Type Tensorial Norm Inequalities for Continuous Functions of Selfadjoint Operators in Hilbert Spaces
    Stojiljkovic, Vuk
    EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2023, 16 (03): : 1421 - 1433
  • [36] Weighted Lebesgue and BMOγ norm inequalities for the Calderon and Hilbert operators
    Ferreyra, Elida, V
    Flores, Guillermo J.
    Viviani, Beatriz E.
    MATHEMATISCHE ZEITSCHRIFT, 2020, 294 (1-2) : 503 - 518
  • [37] Q-NORM INEQUALITIES FOR SEQUENCES OF HILBERT SPACE OPERATORS
    Dragomir, S. S.
    Moslehian, M. S.
    Sandor, J.
    JOURNAL OF MATHEMATICAL INEQUALITIES, 2009, 3 (01): : 1 - 14
  • [38] Generalized spectral radius and norm inequalities for Hilbert space operators
    Abu-Omar, Amer
    Kittaneh, Fuad
    INTERNATIONAL JOURNAL OF MATHEMATICS, 2015, 26 (12)
  • [39] Norm inequalities for vector valued random series
    Sagher, Y
    Xiang, N
    ILLINOIS JOURNAL OF MATHEMATICS, 1996, 40 (04) : 535 - 552
  • [40] Weighted norm inequalities, embedding theorems and integration operators on vector-valued Fock spaces
    Chen, Jiale
    Wang, Maofa
    MATHEMATISCHE ZEITSCHRIFT, 2024, 307 (02)
12345