Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 7, Number 1 (2016), 102-117.
Recent developments of matrix versions of the arithmetic–geometric mean inequality
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.
Ann. Funct. Anal. Volume 7, Number 1 (2016), 102-117.
Received: 25 March 2015
Accepted: 26 May 2015
First available in Project Euclid: 27 November 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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.)
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