Some Reverses of the Jensen Inequality for Functions of Selfadjoint Operators in Hilbert Spaces

Some Reverses of the Jensen Inequality for Functions of Selfadjoint Operators in Hilbert Spaces

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Some Slater Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces

Some inequalities of the Slater type for convex functions of selfad-joint operators in Hilbert spaces H under suitable assumptions for the involved operators are given. Amongst others, it is shown that if A is a positive definite operator with Sp (A) ⊂ [m, M ] and f is convex and has a continuous derivative on [m, M ] , then for any x ∈ H with x = 1 the following inequality holds: 0 ≤ f Af ′ (A...

Some Trapezoidal Vector Inequalities for Continuous Functions of Selfadjoint Operators in Hilbert Spaces

and Applied Analysis 3 where ‖ · ‖p p ∈ 1,∞ are the Lebesgue norms, that is, ∥∥f ′∥∞ ess sup s∈ a,b ∣∣f ′ s ∣∣, ∥∥f ′∥∥ p : (∫b a ∣∣f ′ s ∣∣ds)1/p, p ≥ 1. 1.6 The case of convex functions is as follows 4 . Theorem 1.5. Let f : a, b → be a convex function on a, b . Then one has the inequalities 1 8 b − a 2 [ f ′ ( a b 2 ) − f ′ − ( a b 2 )] ≤ f a f b 2 b − a − ∫b

Some Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces

Some inequalities for convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided.