An extension of Jensen’s operator inequality and its application to Young inequality

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 ...

An Operator Extension of C̆ebys̆ev Inequality

Some operator inequalities for synchronous functions that are related to the c̆ebys̆ev inequality are given. Among other inequalities for synchronous functions it is shown that ‖φ (f (A) g (A))− φ (f (A))φ (g (A))‖ ≤ max {∥∥φ (f2 (A))− φ (f (A))∥∥ , ∥∥φ (g2 (A))− φ (g (A))∥∥} whereA is a self-adjoint and compact operator on B (H ), f, g ∈ C (sp (A)) continuous and non-negative functions and φ : B...