Some Vector Inequalities for Continuous Functions of Self-Adjoint Operators in Hilbert Spaces
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:10.1155/2011/564836Published: 15 March 2011
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.