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.

scholarly journals A numerical radius version of the arithmetic-geometric mean of operators

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2139-2145
Author(s):  
Alemeh Sheikhhosseini
Keyword(s):  
Geometric Mean ◽  
Positive Definite ◽  
Operator Norm ◽  
Numerical Radius ◽  
Positive Definite Operators ◽  
Inequalities For Operators

In this paper, we obtain some numerical radius inequalities for operators, in particular for positive definite operators A; B a numerical radius and some operator norm versions for arithmeticgeometric mean inequality are obtained, respectively as ?2(A#B)? ? (A2+B2/2)- 1/2inf ||x||=1 ?(x), where ?(x) = ?(A - B)x,x?2, and ||A||||B|| ? 1/2 (||A2||+||B2||)-1/2 inf ||x||=||y||=1 ?(x,y), where, ?(x,y) = (?Ay,y? - ?Bx,x?)2.

scholarly journals Maps on positive definite operators preserving the quantum $$\chi _\alpha ^2$$ χ α 2 -divergence

2017 ◽  
Vol 107 (12) ◽  
pp. 2267-2290 ◽  
Author(s):  
Hong-Yi Chen ◽  
György Pál Gehér ◽  
Chih-Neng Liu ◽  
Lajos Molnár ◽  
Dániel Virosztek ◽  
...  
Keyword(s):  
Positive Definite ◽  
Positive Definite 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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