Selfadjoint operators in S-spaces

Non-selfadjoint Perturbations of Selfadjoint Operators in 2 Dimensions I

This is the first in a series of works devoted to small non-selfadjoint perturbations of selfadjoint h-pseudodifferential operators in dimension 2. In the present work we treat the case when the classical flow of the unperturbed part is periodic and the strength ǫ of the perturbation is ≫ h (or sometimes only ≫ h2) and bounded from above by hδ for some δ > 0. We get a complete asymptotic descri...

Sums of Regular Selfadjoint Operators

This is an unedited transscript of the handwritten notes of my talk at the Master Class.

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

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