A survey of Jensen type inequalities for functions of selfadjoint operators in Hilbert spaces

Abstract

a b s t r a c tThe main aim of the present paper is to survey different inequalities for convex functions of selfadjoint operators in Hilbert spaces which have appeared recently in the literature. Applications for some particular convex functions of interest are also given.

On some new converses of convex inequalities in Hilbert space

“…For more on the Mond-Pečarić inequality, i.e. Jensen's inequality for selfadjoint operators and it's refinements, converses and applications, see [1], [4], [5], [6], [11], [12] and [13].…”

Operator Popoviciu’s inequality for superquadratic and convex functions of selfadjoint operators in Hilbert spaces

“…For more recent results concerning inequalities for selfadjoint operatos and other related result, we suggest [2], [4]- [12], [16], [19] and [22].…”

Trace Operator Inequality for Superquadratic Functions

“…For more details, recent result and generalization the reader may refer to [4], [5] and [8]. Related operator inequalities can be found in [6], [7], [10] and [14]- [16].…”