Cauchy-Schwarz inequality in semi-inner product C*-modules via polar decomposition

被引：17
|
作者：
Fujii, J. I. [2 ]
Fujii, M. [3 ]
Moslehian, M. S. [1 ]
Seo, Y. [4 ]
机构：
[1] Ferdowsi Univ Mashhad, CEAAS, Dept Pure Math, Mashhad 91775, Iran
[2] Osaka Kyoiku Univ, Dept Art & Sci Informat Sci, Osaka 5828582, Japan
[3] Osaka Kyoiku Univ, Dept Math, Osaka 5828582, Japan
[4] Shibaura Inst Technol, Coll Engn, Minuma Ku, Saitama 3378570, Japan
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 394卷 / 02期
关键词：
Hilbert C*-module; Operator inequality; Operator geometric mean; Positive operator; Kantorovich inequality;
D O I：
10.1016/j.jmaa.2012.04.083
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
By virtue of the operator geometric mean and the polar decomposition, we present a new Cauchy-Schwarz inequality in the framework of semi-inner product C*-modules over unital C*-algebras and discuss the equality case. We also give several additive and multiplicative type reverses of it. As an application, we present a Kantorovich type inequality on a Hilbert C*-module. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：835 / 840
页数：6
相关论文
共 25 条
  • [1] ON THE CAUCHY-SCHWARZ INEQUALITY AND ITS REVERSE IN SEMI-INNER PRODUCT C*-MODULES
    Ilisevic, Dijana
    Varosanec, Sanja
    BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2007, 1 (01): : 78 - 84
  • [2] A treatment of the Cauchy-Schwarz inequality in C*-modules
    Arambasic, Ljiljana
    Bakic, Damir
    Moslehian, Mohammad Sal
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 381 (02) : 546 - 556
  • [3] OPERATOR INEQUALITIES ON HILBERT C*-MODULES VIA THE CAUCHY-SCHWARZ INEQUALITY
    Fujii, Jun Ichi
    Fujii, Masatoshi
    Seo, Yuki
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2014, 17 (01): : 295 - 315
  • [4] Characterizations of inner product spaces via angular distances and Cauchy-Schwarz inequality
    Krnic, Mario
    Minculete, Nicusor
    AEQUATIONES MATHEMATICAE, 2021, 95 (01) : 147 - 166
  • [5] ON THE CAUCHY-SCHWARZ INEQUALITY AND SEVERAL INEQUALITIES IN AN INNER PRODUCT SPACE
    Minculete, Nicusor
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2019, 22 (04): : 1137 - 1144
  • [6] On the Cauchy-Schwarz inequality and its reverse in 2-*-semi inner product spaces
    Najmabadi, B. Mohebbi
    Shateri, T. L.
    ARABIAN JOURNAL OF MATHEMATICS, 2020, 9 (01) : 145 - 153
  • [7] Some Improvements of the Cauchy-Schwarz Inequality Using the Tapia Semi-Inner-Product
    Minculete, Nicusor
    Moradi, Hamid Reza
    MATHEMATICS, 2020, 8 (12) : 1 - 13
  • [8] Reverse Cauchy-Schwarz type inequalities in pre-inner product C*-modules
    Fujii, Jun-Ichi
    Fujii, Masatoshi
    Moslehian, Mohammad Sal
    Pecaric, Josip E.
    Seo, Yuki
    HOKKAIDO MATHEMATICAL JOURNAL, 2011, 40 (03) : 393 - 409
  • [9] Some Results on Reverses of Cauchy-Schwarz Inequality in Inner Product Spaces
    王公宝
    马吉溥
    NortheasternMathematicalJournal, 2005, (02) : 207 - 211
  • [10] Refinements of the Cauchy-Schwarz inequality in pre-Hilbert C*-modules and their applications
    Zamani, Ali
    ANNALS OF FUNCTIONAL ANALYSIS, 2023, 14 (04)
123