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

页码：835 / 840

页数：6

共 5 条

[1] OPERATOR INEQUALITIES ON HILBERT C*-MODULES VIA THE CAUCHY-SCHWARZ INEQUALITY
Fujii, Jun Ichi
Fujii, Masatoshi
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MATHEMATICAL INEQUALITIES & APPLICATIONS, 2014, 17 (01): : 295 - 315
[2] A treatment of the Cauchy-Schwarz inequality in C*-modules
Arambasic, Ljiljana
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Moslehian, Mohammad Sal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 381 (02) : 546 - 556
[3] Reverse Cauchy-Schwarz type inequalities in pre-inner product C*-modules
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Fujii, Masatoshi
Moslehian, Mohammad Sal
Pecaric, Josip E.
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HOKKAIDO MATHEMATICAL JOURNAL, 2011, 40 (03) : 393 - 409
[4] C*-module operators which satisfy the generalized Cauchy-Schwarz type inequality
Zamani, Ali
LINEAR & MULTILINEAR ALGEBRA, 2024, 72 (04) : 644 - 654
[5] Buzano Inequality in Inner Product C*-modules via the Operator Geometric Mean
Fujii, Jun Ichi
Fujii, Masatoshi
Seo, Yuki
FILOMAT, 2015, 29 (08) : 1689 - 1694

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