Operator upper bounds for Davis-Choi-Jensen's difference in Hilbert spaces

Abstract

In this paper we obtain several operator inequalities providing upper bounds for the Davis-Choi-Jensen's Difference Ph (f (A)) - f (Ph (A)) for any convex function f : I → R, any selfadjoint operator A in H with the spectrum Sp (A) ⊂ I and any linear, positive and normalized map Ph : B (H) → B (K), where H and K are Hilbert spaces. Some examples of convex and operator convex functions are also provided.

Keywords

• selfadjoint bounded linear operators
• functions of operators
• operator convex functions
• jensen's operator inequality
• linear
• positive and normalized map