Some Vector Inequalities for Continuous Functions of Self-Adjoint Operators in Hilbert Spaces
نویسندگان
چکیده
منابع مشابه
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
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Let T be a continuous linear map V → V for a (separable) Hilbert space V . Its spectrum σ(T ) is a compact subset of R, so is certainly contained in some finite interval [a, b]. As usual, for a self-adjoint continuous operator S on V , write S ≥ 0 when 〈Sv, v〉 ≥ 0 for all v ∈ V . For self-adjoint S, T , write S ≤ T when T − S ≥ 0. At the outset, with a ≤ −|T |op and b ≥ |T |op, we have, 〈a · v,...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2011
ISSN: 1029-242X
DOI: 10.1155/2011/564836