scholarly journals Matrix and Operator Trace Inequalities

Scholarpedia ◽  
2013 ◽  
Vol 8 (4) ◽  
pp. 30919 ◽  
Author(s):  
Anna Vershynina ◽  
Eric Carlen ◽  
Elliott Lieb
Author(s):  
Mohammad Alomari

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.


2020 ◽  
Vol 23 (5) ◽  
pp. 1452-1471
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi

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.


Author(s):  
Xinmin Yang

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


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

2011 ◽  
Vol 225-226 ◽  
pp. 970-973
Author(s):  
Shi Qing Wang

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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