Open Access Research Article

Some Vector Inequalities for Continuous Functions of Self-Adjoint Operators in Hilbert Spaces

SS Dragomir

Author Affiliations

Mathematics, School of Engineering & Science, Victoria University, P.O. Box 14428, Melbourne City, VIC 8001, Australia

School of Computational & Applied Mathematics, University of the Witwatersrand, Private Bag-3, Johannesburg 2050, South Africa

Journal of Inequalities and Applications 2011, 2011:564836  doi:10.1155/2011/564836

Published: 15 March 2011

Abstract

On utilizing the spectral representation of self-adjoint operators in Hilbert spaces, some inequalities for the composite operator , where and for various classes of continuous functions are given. Applications for the power function and the logarithmic function are also provided.