Annals of Functional Analysis

Recent developments of matrix versions of the arithmetic–geometric mean inequality

Jun Ichi Fujii, Masatoshi Fujii, Yuki Seo, and Hongliang Zuo

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Abstract

The main aim of this survey article is to present recent developments of matrix versions of the arithmetic–geometric mean inequality. Among others, we show improvements and generalizations of the arithmetic–geometric mean inequality for unitarily invariant norms via the Hadamard product, and for singular values via the operator monotone functions.

Article information

Source
Ann. Funct. Anal. Volume 7, Number 1 (2016), 102-117.

Dates
Received: 25 March 2015
Accepted: 26 May 2015
First available in Project Euclid: 27 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.afa/1448591838

Digital Object Identifier
doi:10.1215/20088752-3429400

Mathematical Reviews number (MathSciNet)
MR3449343

Zentralblatt MATH identifier
1357.47017

Subjects
Primary: 47A63: Operator inequalities
Secondary: 15A18: Eigenvalues, singular values, and eigenvectors 15A42: Inequalities involving eigenvalues and eigenvectors 47A30: Norms (inequalities, more than one norm, etc.)

Keywords
arithmetic–geometric mean inequality Heinz inequality unitarily invariant norm singular value Hadamard product

Citation

Fujii, Jun Ichi; Fujii, Masatoshi; Seo, Yuki; Zuo, Hongliang. Recent developments of matrix versions of the arithmetic–geometric mean inequality. Ann. Funct. Anal. 7 (2016), no. 1, 102--117. doi:10.1215/20088752-3429400. https://projecteuclid.org/euclid.afa/1448591838


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