Banach Journal of Mathematical Analysis

Refinements of quasi-arithmetic means inequalities for Hilbert space operators

Jadranka Mićić

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Abstract

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

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

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1419000581

Digital Object Identifier
doi:10.15352/bjma/09-1-9

Mathematical Reviews number (MathSciNet)
MR3296089

Zentralblatt MATH identifier
06430408

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

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

Citation

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. https://projecteuclid.org/euclid.bjma/1419000581


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