Resumen de Some Slater type inequalities for convex functions of selfadjoint operators in Hilbert spaces

Sever Silvestru Dragomir

• Some inequalities of the Slater type for convex functions of selfadjoint operators in Hilbert spaces H under suitable assumptions for the involved operators are given. Amongst others, it is shown that if A is a positive definite operator with Sp (A) ⊂ [m, M] and f is convex and has a continuous derivative on [m, M] , then for any x ∈ H with kxk = 1 the following inequality holds.