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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:394

Article

Fujii, J. I.²  Fujii, M.³  Moslehian, M. S.¹  Seo, Y.⁴ 

[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

关键词: Hilbert C*-module;    Operator inequality;    Operator geometric mean;    Positive operator;    Kantorovich inequality;   

DOI  :  10.1016/j.jmaa.2012.04.083

来源: Elsevier

【 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.

【 授权许可】

Free