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INEQUALITIES OF JENSEN’S TYPE FOR POSITIVE LINEAR FUNCTIONALS ON HERMITIAN UNITAL BANACH $\ast$-ALGEBRAS

Part of: General theory of linear operators Inequalities Basic linear algebra

Published online by Cambridge University Press:  08 January 2020

S. S. DRAGOMIR Open the ORCID record for S. S. DRAGOMIR [Opens in a new window]
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

We establish inequalities of Jensen’s and Slater’s type in the general setting of a Hermitian unital Banach $\ast$-algebra, analytic convex functions and positive normalised linear functionals.

Keywords

Hermitian unital Banach ∗-algebrapositive linear functionalinequalities for the power functionJensen’s type inequalities

MSC classification

Primary: 47A63: Operator inequalities
Secondary: 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory 26D15: Inequalities for sums, series and integrals 26D10: Inequalities involving derivatives and differential and integral operators 47A30: Norms (inequalities, more than one norm, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 2 , October 2020 , pp. 308 - 318
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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