Some Inequalities for Selfadjoint Operators on Quaternionic Hilbert Spaces

2019 ◽  
Vol 30 (1) ◽  
Author(s):  
S. Mahdipour ◽  
A. Niknam ◽  
M. Fashandi
Keyword(s):  
Hilbert Spaces ◽  
Selfadjoint Operators

scholarly journals Operator Popoviciu’s inequality for superquadratic and convex functions of selfadjoint operators in Hilbert spaces

2019 ◽  
Vol 10 (4) ◽  
pp. 313-324
Author(s):  
Mohammad W. Alomari
Keyword(s):  
Hilbert Spaces ◽  
Convex Functions ◽  
Positive Operators ◽  
Selfadjoint Operators ◽  
Popoviciu’S Inequality ◽  
Linear Maps ◽  
Superquadratic Functions ◽  
Operator Version ◽  
Positive Linear Maps

AbstractIn this work, an operator version of Popoviciu’s inequality for positive operators on Hilbert spaces under positive linear maps for superquadratic functions is proved. Analogously, using the same technique, an operator version of Popoviciu’s inequality for convex functions is obtained. Some other related inequalities are also presented.

scholarly journals AN INFINITE DIMENSIONAL VERSION OF THE SCHUR CONVEXITY PROPERTY AND APPLICATIONS

2007 ◽  
Vol 05 (02) ◽  
pp. 123-136 ◽  
Author(s):  
CLAUDE VALLÉE ◽  
VICENŢIU RĂDULESCU
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Symmetric Matrix ◽  
Liouville Problem ◽  
Convexity Property ◽  
Infinite Dimensional ◽  
Selfadjoint Operators ◽  
Dimensional Version ◽  
Sturm Liouville ◽  
Schur Convexity

We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of linear selfadjoint operators that can be approximated by operators of finite rank and having a countable family of eigenvalues. The abstract results of the present paper are illustrated by several examples from mechanics or quantum mechanics, including the Sturm–Liouville problem, the Schrödinger equation, and the harmonic oscillator.

scholarly journals Reverse Jensen’s type Trace Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces

2016 ◽  
Vol 30 (1) ◽  
pp. 39-62
Author(s):  
Sever S. Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Convex Functions ◽  
Selfadjoint Operators ◽  
Trace Inequalities

AbstractSome reverse Jensen’s type trace inequalities for convex functions of selfadjoint operators in Hilbert spaces are provided. Applications for some convex functions of interest and reverses of Hölder and Schwarz trace inequalities are also given.

Refinements of the weighted generalized trapezoid inequality in terms of cumulative variation and applications

2018 ◽  
Vol 25 (1) ◽  
pp. 47-64 ◽  
Author(s):  
Wenjun Liu ◽  
Heng Zhang
Keyword(s):  
Bounded Variation ◽  
Hilbert Spaces ◽  
Functions Of Bounded Variation ◽  
Selfadjoint Operators ◽  
Trapezoid Inequality ◽  
Variation Function

AbstractIn this paper, we first establish some refinements of the weighted generalized trapezoid inequality for functions of bounded variation in terms of a cumulative variation function, and then obtain some perturbed versions of the weighted generalized trapezoid inequality. Several applications for selfadjoint operators on complex Hilbert spaces are also given.

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

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Spectral Representation ◽  
Continuous Functions ◽  
Selfadjoint Operators

On utilising the spectral representation of selfadjoint operators in Hilbert spaces, some trapezoidal inequalities for various classes of continuous functions of such operators are given.

scholarly journals New bounds for the Cebysev functional of two functions of selfadjoint operators in Hilbert spaces

Filomat ◽  
2010 ◽  
Vol 24 (2) ◽  
pp. 27-39 ◽  
Author(s):  
S.S. Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Selfadjoint Operators ◽  
Čebyšev Functional ◽  
Subject Classifications ◽  
Mathematics Subject Classifications ◽  
New Inequalities

Some new inequalities for the Cebysev functional of two functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved functions and operators, are given. 2010 Mathematics Subject Classifications. 47A63; 47A99. .

scholarly journals Cebysev’s type inequalities and power inequalities for the Berezin number of operators

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2307-2316
Author(s):  
Mubariz Garayev ◽  
Ulaş Yamancı
Keyword(s):  
Hilbert Spaces ◽  
Convex Functions ◽  
Reproducing Kernel ◽  
Type Inequality ◽  
Reproducing Kernel Hilbert Spaces ◽  
Selfadjoint Operators ◽  
Kernel Hilbert Spaces ◽  
Berezin Number

We give operator analogues of some classical inequalities, including Cebysev type inequality for synchronous and convex functions of selfadjoint operators in Reproducing Kernel Hilbert Spaces (RKHSs). We obtain some Berezin number inequalities for the product of operators. Also, we prove the Berezin number inequality for the commutator of two operators.

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