Korean J. Math. Vol. 24 No. 2 (2016) pp.273-296
DOI: https://doi.org/10.11568/kjm.2016.24.2.273

Some trace inequalities for convex functions of selfadjoint operators in Hilbert spaces

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Published: Jun 30, 2016
Keywords:
Trace class operators, Hilbert-Schmidt operators, Trace, Convex functions, Jensen’s inequality, Trace inequalities for matrices, Power series of operators.
Mathematics Subject Classification:
Jensen’s inequality, 47A63, 47A99.

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Silvestru Sever Dragomir
Mathematics, College of Engineering & Science Victoria University, PO Box 14428 Melbourne City, MC 8001, Australia.

Abstract

Some new trace inequalities for convex functions of selfadjoint operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated. Some trace inequalities for matrices are also derived. Examples for the operator power and logarithm are presented as well.


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