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On superquadratic functions of Hilbert space operators

On superquadratic functions of Hilbert space operators J Anal https://doi.org/10.1007/s41478-018-0106-5 ORIGINAL RESEARCH PAPER Mohsen Kian Received: 15 February 2018 / Accepted: 2 June 2018 © Forum D’Analystes, Chennai 2018 Abstract Some inequalities involving superquadratic functions for Hilbert space operators are presented. In particular, we refine some results concerning convex functions by considering nonnegative superquadratic functions. Some applications to special functions are given as well. Keywords Superquadratic function · Self-adjoint operator · Convex function Mathematics Subject Classification 47A63 · 26D15 1 Introduction In what follows let (ℋ) be the C -algebra of all bounded linear operators on a Hil- bert space ℋ and 1 be the identity operator. An operator A is said to be positive (denoted by A ≥ 0 ) if ⟨Ax, x⟩ ≥ 0 for all x ∈ ℋ . Let f ∶ J → ℝ be a continuous function. We put (J) to be the set of all self-adjoint operators on ℋ with spectrum contained in J. For A ∈ (J) , we mean by f(A), the continuous functional calculus of f at A. A function f ∶[0, ∞) → ℝ is said to be superquadratic provided that for all a ≥ 0 there exists a constant C ∈ ℝ such that f (b) ≥ f (a)+ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Analysis Springer Journals

On superquadratic functions of Hilbert space operators

The Journal of Analysis , Volume OnlineFirst – Jun 11, 2018

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Forum D'Analystes, Chennai
Subject
Mathematics; Analysis; Functional Analysis; Abstract Harmonic Analysis; Special Functions; Fourier Analysis; Measure and Integration
ISSN
0971-3611
eISSN
2367-2501
DOI
10.1007/s41478-018-0106-5
Publisher site
See Article on Publisher Site

Abstract

J Anal https://doi.org/10.1007/s41478-018-0106-5 ORIGINAL RESEARCH PAPER Mohsen Kian Received: 15 February 2018 / Accepted: 2 June 2018 © Forum D’Analystes, Chennai 2018 Abstract Some inequalities involving superquadratic functions for Hilbert space operators are presented. In particular, we refine some results concerning convex functions by considering nonnegative superquadratic functions. Some applications to special functions are given as well. Keywords Superquadratic function · Self-adjoint operator · Convex function Mathematics Subject Classification 47A63 · 26D15 1 Introduction In what follows let (ℋ) be the C -algebra of all bounded linear operators on a Hil- bert space ℋ and 1 be the identity operator. An operator A is said to be positive (denoted by A ≥ 0 ) if ⟨Ax, x⟩ ≥ 0 for all x ∈ ℋ . Let f ∶ J → ℝ be a continuous function. We put (J) to be the set of all self-adjoint operators on ℋ with spectrum contained in J. For A ∈ (J) , we mean by f(A), the continuous functional calculus of f at A. A function f ∶[0, ∞) → ℝ is said to be superquadratic provided that for all a ≥ 0 there exists a constant C ∈ ℝ such that f (b) ≥ f (a)+

Journal

The Journal of AnalysisSpringer Journals

Published: Jun 11, 2018

References