Extension of Jensen's Inequality for Operators without Operator Convexity

Extension of Jensen’s Inequality for Operators without Operator Convexity

and Applied Analysis 3 If one of the following conditions ii ψ ◦ φ−1 is concave and ψ−1 is operator monotone, ii′ ψ ◦ φ−1 is convex and −ψ−1 is operator monotone, is satisfied, then the reverse inequality is valid in 1.7 . In this paper we study an extension of Jensen’s inequality given in Theorem A. As an application of this result, we give an extension of Theorem B for a version of the quasia...

An Operator Extension of Bohr's inequality

An Extension of Chebyshevs Inequality and Its Connection with Jensens Inequality

The aim of this paper is to show that Jensen’s Inequality and an extension of Chebyshev’s Inequality complement one another, so that they both can be formulated in a pairing form, including a second inequality, that provides an estimate for the classical one. 1. Introduction The well known fact that the derivative and the integral are inverse each other has a lot of interesting consequences, on...

an operator extension of bohr's inequality

An Operator Extension of Bohr’s Inequality

T φ(At)dμ(t) for every linear functional φ in the norm dual A of A; cf. [3, Section 4.1]. Further, a field (φt)t∈T of positive linear mappings φ : A → B between C -algebras of operators is called continuous if the function t 7→ φt(A) is continuous for every A ∈ A. If the C-algebras include the identity operators, denoted by the same I, and the field t 7→ φt(I) is integrable with integral I, we ...