Extension of the refined Jensen's operator inequality with condition on spectra

This is a submission to one of journals of TMRG: BJMA/AFA EXTENSION OF THE REFINED JENSEN’S OPERATOR INEQUALITY WITH CONDITION ON SPECTRA

We give an extension of the refined Jensen’s operator inequality for n−tuples of self-adjoint operators, unital n−tuples of positive linear mappings and real valued continuous convex functions with conditions on the spectra of the operators. We also study the order among quasi-arithmetic means under similar conditions.

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 ...