Banach Journal of Mathematical Analysis

Refinements of quasi-arithmetic means inequalities for Hilbert space operators

Jadranka Mićić

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In this paper some inequalities involving quasi-arithmetic means for a continuous field of self-adjoint operators, a field of positive linear mappings and continuous strictly monotone functions are refined. These refined converses are presented by using the Mond-Pečarić method improvement. Obtained results are applied to refine selected inequalities with power functions.

Article information

Banach J. Math. Anal., Volume 9, Number 1 (2015), 111-126.

First available in Project Euclid: 19 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A63: Operator inequalities
Secondary: 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.) 47A64: Operator means, shorted operators, etc.

Quasi-arithmetic mean power mean self-adjoint operator positive linear mapping Jensen's operator inequality


Mićić, Jadranka. Refinements of quasi-arithmetic means inequalities for Hilbert space operators. Banach J. Math. Anal. 9 (2015), no. 1, 111--126. doi:10.15352/bjma/09-1-9.

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