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
  • [1] Norm and Numerical Radius Inequalities for Sums of Power Series of Operators in Hilbert Spaces
    Altwaijry, Najla
    Dragomir, Silvestru Sever
    Feki, Kais
    AXIOMS, 2024, 13 (03)
  • [2] Some Inequalities for Power Series of Two Operators in Hilbert Spaces
    Dragomir, Sever Silvestru
    Uchiyama, Mitsuru
    TOKYO JOURNAL OF MATHEMATICS, 2013, 36 (02) : 483 - 498
  • [3] Some numerical radius inequalities for power series of operators in Hilbert spaces
    Dragomir, Silvestru Sever
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,
  • [4] Some numerical radius inequalities for power series of operators in Hilbert spaces
    Silvestru Sever Dragomir
    Journal of Inequalities and Applications, 2013
  • [5] Hölder-Type Inequalities for Power Series of Operators in Hilbert Spaces
    Altwaijry, Najla
    Dragomir, Silvestru Sever
    Feki, Kais
    AXIOMS, 2024, 13 (03)
  • [6] SOME INEQUALITIES FOR THE NORM AND THE NUMERICAL RADIUS OF LINEAR OPERATORS IN HILBERT SPACES
    Dragomir, S. S.
    TAMKANG JOURNAL OF MATHEMATICS, 2008, 39 (01): : 1 - 7
  • [7] VECTOR INEQUALITIES FOR POWERS OF SOME OPERATORS IN HILBERT SPACES
    Dragomir, S. S.
    FILOMAT, 2009, 23 (01) : 69 - 83
  • [8] INEQUALITIES FOR POWER SERIES OF PRODUCT OF OPERATORS IN HILBERT SPACES WITH APPLICATIONS TO NUMERICAL RADIUS
    Dragomir, Silvestru Sever
    Garayev, Mubariz Tapdigoglu
    JOURNAL OF MATHEMATICAL INEQUALITIES, 2024, 18 (03): : 1007 - 1028
  • [9] INEQUALITIES FOR TWO POWER SERIES OF NONCOMMUTATIVE OPERATORS IN HILBERT SPACES WITH APPLICATIONS TO NUMERICAL RADIUS
    Dragomir, Silvestru Sever
    Garayev, Mubariz Tapdigoglu
    JOURNAL OF MATHEMATICAL INEQUALITIES, 2025, 19 (01): : 99 - 118
  • [10] Some inequalities for power series of selfadjoint operators in Hilbert spaces via reverses of the Schwarz inequality
    Dragomir, S. S.
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2009, 20 (10) : 757 - 767
12345