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February 2016 Recent developments of matrix versions of the arithmetic–geometric mean inequality
Jun Ichi Fujii, Masatoshi Fujii, Yuki Seo, Hongliang Zuo
Ann. Funct. Anal. 7(1): 102-117 (February 2016). DOI: 10.1215/20088752-3429400

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.

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Jun Ichi Fujii. Masatoshi Fujii. Yuki Seo. Hongliang Zuo. "Recent developments of matrix versions of the arithmetic–geometric mean inequality." Ann. Funct. Anal. 7 (1) 102 - 117, February 2016. https://doi.org/10.1215/20088752-3429400

Information

Received: 25 March 2015; Accepted: 26 May 2015; Published: February 2016
First available in Project Euclid: 27 November 2015

zbMATH: 1357.47017
MathSciNet: MR3449343
Digital Object Identifier: 10.1215/20088752-3429400

Subjects:
Primary: 47A63
Secondary: 15A18‎ , 15A42 , 47A30

Keywords: arithmetic–geometric mean inequality , Hadamard product , Heinz inequality , Singular value , ‎unitarily invariant norm

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.7 • No. 1 • February 2016
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