scholarly journals Trace Operator Inequality for Superquadratic Functions

2019 ◽  
Author(s):  
Mohammad Alomari
Keyword(s):  
Hilbert Space ◽  
Operator Inequality ◽  
Trace Operator ◽  
Trace Inequality ◽  
Hermitian Matrices ◽  
Linear Map ◽  
Hilbert Space Operators ◽  
Superquadratic Functions ◽  
Trace Inequalities ◽  
Operator Trace

In this work, some operator trace inequalities are proved. An extension of Klein's inequality for all Hermitian matrices is proved. A non-commutative version (or Hansen-Pedersen version) of the Jensen trace inequality is provided as well. A generalization of the result for any positive Hilbert space operators acts on a positive unital linear map is established.

scholarly journals Operator Jensen's Inequality for Operator Superquadratic Functions

2019 ◽  
Author(s):  
Mohammad W. Alomari
Keyword(s):  
Hilbert Space ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Linear Map ◽  
Superquadratic Function ◽  
Hilbert Space Operators ◽  
Superquadratic Functions

In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. Equivalent statements of a non-commutative version of Jensen's inequality for operator superquadratic function are established. A generalization of the main result to any positive unital linear map is also provided.

scholarly journals Some mappings related to Levinson’s inequality for Hilbert space operators

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1995-2009 ◽  
Author(s):  
Jadranka Micic ◽  
Josip Pecaric
Keyword(s):  
Hilbert Space ◽  
Operator Inequality ◽  
Jensen Inequality ◽  
Hilbert Space Operators ◽  
Levinson’S Inequality

We observe properties of some mappings related to the Davis-Choi-Jensen inequality for Hilbert space operators. Using these results, we observe properties of some mappings related to Levinson?s operator inequality. Consequently, we obtain several refinements for each of these inequalities.

Operator m-convex functions

2018 ◽  
Vol 25 (1) ◽  
pp. 93-107
Author(s):  
Jamal Rooin ◽  
Akram Alikhani ◽  
Mohammad Sal Moslehian
Keyword(s):  
Hilbert Space ◽  
Convex Functions ◽  
Weight Functions ◽  
Operator Inequality ◽  
Jensen Inequality ◽  
Hilbert Space Operators ◽  
Operator Version ◽  
Continuous Fields ◽  
Adjoint Operators ◽  
Comprehensive Study

AbstractThe aim of this paper is to present a comprehensive study of operatorm-convex functions. Let{m\in[0,1]}, and{J=[0,b]}for some{b\in\mathbb{R}}or{J=[0,\infty)}. A continuous function{\varphi\colon J\to\mathbb{R}}is called operatorm-convex if for any{t\in[0,1]}and any self-adjoint operators{A,B\in\mathbb{B}({\mathscr{H}})}, whose spectra are contained inJ, we have{\varphi(tA+m(1-t)B)\leq t\varphi(A)+m(1-t)\varphi(B)}. We first generalize the celebrated Jensen inequality for continuousm-convex functions and Hilbert space operators and then use suitable weight functions to give some weighted refinements. Introducing the notion of operatorm-convexity, we extend the Choi–Davis–Jensen inequality for operatorm-convex functions. We also present an operator version of the Jensen–Mercer inequality form-convex functions and generalize this inequality for operatorm-convex functions involving continuous fields of operators and unital fields of positive linear mappings. Employing the Jensen–Mercer operator inequality for operatorm-convex functions, we construct them-Jensen operator functional and obtain an upper bound for it.

scholarly journals Some Refinements of the Numerical Radius Inequalities via Young Inequality

2021 ◽  
Vol 45 (02) ◽  
pp. 191-202
Author(s):  
Z. HEYDARBEYGI ◽  
M. AMYARI
Keyword(s):  
Hilbert Space ◽  
Young Inequality ◽  
Operator Inequality ◽  
Numerical Radius ◽  
Hilbert Space Operators

In this paper, we get an improvement of the Hölder-McCarthy operator inequality in the case when r ≥ 1 and refine generalized inequalities involving powers of the numerical radius for sums and products of Hilbert space operators.

scholarly journals Bounded point evaluations for cyclic Hilbert space operators

2003 ◽  
Vol 4 (2) ◽  
pp. 301
Author(s):  
A. Bourhim
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Bounded Linear ◽  
Hilbert Space Operators ◽  
Point Evaluations ◽  
Analytic Bounded Point Evaluations

<p>In this talk, to be given at a conference at Seconda Università degli Studi di Napoli in September 2001, we shall describe the set of analytic bounded point evaluations for an arbitrary cyclic bounded linear operator T on a Hilbert space H and shall answer some questions due to L. R. Williams.</p>

scholarly journals Eigenvalue inequalities for differences of means of Hilbert space operators

2012 ◽  
Vol 436 (5) ◽  
pp. 1516-1527 ◽  
Author(s):  
Omar Hirzallah ◽  
Fuad Kittaneh ◽  
Mario Krnić ◽  
Neda Lovričević ◽  
Josip Pečarić
Keyword(s):  
Hilbert Space ◽  
Hilbert Space Operators

A Trace Inequality for Symmetric Nonnegative Definite Matrices

2011 ◽  
Vol 225-226 ◽  
pp. 970-973
Author(s):  
Shi Qing Wang
Keyword(s):  
Control Theory ◽  
Communication Systems ◽  
Positive Definite ◽  
Trace Inequality ◽  
Positive Definite Matrices ◽  
Symmetric Positive Definite ◽  
Multiple Input ◽  
Nonnegative Definite ◽  
Symmetric Positive Definite Matrices ◽  
Trace Inequalities

Trace inequalities naturally arise in control theory and in communication systems with multiple input and multiple output. One application of Belmega’s trace inequality has already been identified [3]. In this paper, we extend the symmetric positive definite matrices of his inequality to symmetric nonnegative definite matrices, and the inverse matrices to Penrose-Moore inverse matrices.

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