scholarly journals Matrix and Operator Trace Inequalities

Scholarpedia ◽  
2013 ◽  
Vol 8 (4) ◽  
pp. 30919 ◽  
Author(s):  
Anna Vershynina ◽  
Eric Carlen ◽  
Elliott Lieb
Keyword(s):  
Trace Inequalities ◽  
Operator Trace

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.

Trace inequalities for fractional integrals in mixed norm grand lebesgue spaces

2020 ◽  
Vol 23 (5) ◽  
pp. 1452-1471
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Riesz Potential ◽  
Fractional Integrals ◽  
Mixed Norm ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Grand Lebesgue Spaces ◽  
Measure Spaces ◽  
Necessary And Sufficient ◽  
Bounded Sets ◽  
Trace Inequalities

Abstract D. Adams type trace inequalities for multiple fractional integral operators in grand Lebesgue spaces with mixed norms are established. Operators under consideration contain multiple fractional integrals defined on the product of quasi-metric measure spaces, and one-sided multiple potentials. In the case when we deal with operators defined on bounded sets, the established conditions are simultaneously necessary and sufficient for appropriate trace inequalities. The derived results are new even for multiple Riesz potential operators defined on the product of Euclidean spaces.

scholarly journals Some trace inequalities for operators

1995 ◽  
Vol 58 (2) ◽  
pp. 281-286 ◽  
Author(s):  
Xinmin Yang
Keyword(s):  
Positive Definite ◽  
Positive Definite Operators ◽  
Open Question ◽  
Trace Inequalities ◽  
Inequalities For Operators

AbstractIn this paper, we obtain some trace inequalities for arbitrary finite positive definite operators. Finally an open question is presented.

Trace Inequalities of Sobolev Type in the Upper Triangle Case

2000 ◽  
Vol 80 (2) ◽  
pp. 391-414 ◽  
Author(s):  
Carme Cascante ◽  
Joaquín M. Ortega ◽  
Igor E. Verbitsky
Keyword(s):  
Sobolev Type ◽  
Trace Inequalities

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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