Banach Journal of Mathematical Analysis

Refinements and reverses of means inequalities for Hilbert space operators

Fuad Kittaneh, Mario Krnic, Neda Lovricevic, Josip Pecaric, and Omar Hirzallah

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Abstract

In this paper we derive some improvements of means inequalities for Hilbert space operators. More precisely, we obtain refinements and reverses of the arithmetic-geometric operator mean inequality. As an application, we also deduce an improved variant for the refined arithmetic--Heinz mean inequality. We also present some eigenvalue inequalities for differences of certain operator means.

Article information

Source
Banach J. Math. Anal., Volume 7, Number 2 (2013), 15 -29 .

Dates
First available in Project Euclid: 20 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1363784220

Digital Object Identifier
doi:10.15352/bjma/1363784220

Mathematical Reviews number (MathSciNet)
MR3039936

Zentralblatt MATH identifier
1276.47021

Subjects
Primary: 47A63
Secondary: 47A10 47B06 47B07 47B15 26D20

Keywords
positive operator compact operator operator mean refinement eigenvalue

Citation

Hirzallah , Omar; Kittaneh, Fuad; Krnic, Mario; Lovricevic, Neda; Pecaric, Josip. Refinements and reverses of means inequalities for Hilbert space operators. Banach J. Math. Anal. 7 (2013), no. 2, 15 --29. doi:10.15352/bjma/1363784220. https://projecteuclid.org/euclid.bjma/1363784220


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