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OPERATOR QUASILINEARITY OF SOME FUNCTIONALS ASSOCIATED WITH DAVIS–CHOI–JENSEN’S INEQUALITY FOR POSITIVE MAPS

Part of: General theory of linear operators Basic linear algebra

Published online by Cambridge University Press:  19 October 2016

S. S. DRAGOMIR
S. S. DRAGOMIR*
Affiliation:
Mathematics, College of Engineering and Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa email sever.dragomir@vu.edu.au
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Abstract

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In this paper we establish operator quasilinearity properties of some functionals associated with Davis–Choi–Jensen’s inequality for positive maps and operator convex or concave functions. Applications for the power function and the logarithm are provided.

Keywords

Jensen’s inequalityoperator convex functionsarithmetic mean–geometric mean inequalitysuperadditivitysubadditivity

MSC classification

Primary: 47A63: Operator inequalities
Secondary: 47A30: Norms (inequalities, more than one norm, etc.) 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 2 , April 2017 , pp. 322 - 332
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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