An Operator Extension of Bohr's inequality

an operator extension of bohr's inequality

an operator extension of bohr's inequality

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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...

An Operator Inequality Related to Jensen’s Inequality

For bounded non-negative operators A and B, Furuta showed 0 ≤ A ≤ B implies A r 2BA r 2 ≤ (A r 2BA r 2 ) s+r t+r (0 ≤ r, 0 ≤ s ≤ t). We will extend this as follows: 0 ≤ A ≤ B ! λ C (0 < λ < 1) implies A r 2 (λB + (1− λ)C)A r 2 ≤ {A r 2 (λB + (1 − λ)C)A r 2 } s+r t+r , where B ! λ C is a harmonic mean of B and C. The idea of the proof comes from Jensen’s inequality for an operator convex functio...

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...