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SOME INEQUALITIES OF JENSEN TYPE FOR ARG-SQUARE CONVEX FUNCTIONS OF UNITARY OPERATORS IN HILBERT SPACES

Part of: General theory of linear operators Inequalities

Published online by Cambridge University Press:  12 May 2014

S. S. DRAGOMIR
S. S. DRAGOMIR*
Affiliation:
Mathematics, College of Engineering & Science, Victoria University, PO Box 14428, Melbourne, Victoria 8001, Australia School of Computational & 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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Some inequalities of Jensen type for Arg-square-convex functions of unitary operators in Hilbert spaces are given.

Keywords

Jensen’s inequalityRiemann–Stieltjes integral inequalitiesUnitary operators in Hilbert spacesSpectral theory

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals 47A63: Operator inequalities

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 1 , August 2014 , pp. 65 - 73
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

Dragomir, S. S., ‘Bounds for the normalized Jensen functional’, Bull. Aust. Math. Soc. 74 (2006), 471–476.Google Scholar
Dragomir, S. S., Operator Inequalities of the Jensen, Čebyšev and Grüss Type, Springer Briefs in Mathematics (Springer, New York, 2012).Google Scholar
Dragomir, S. S., Operator Inequalities of Ostrowski and Trapezoidal Type, Springer Briefs in Mathematics (Springer, New York, 2012).Google Scholar
Helmberg, G., Introduction to Spectral Theory in Hilbert Space (John Wiley & Sons, New York, 1969).Google Scholar