Operator Inequalities.

1981 ◽  
Vol 37 (156) ◽  
pp. 600
Author(s):  
Howard A. Levine ◽  
Johann Schroder
Keyword(s):  
Operator Inequalities

Some operator inequalities for unitarily invariant norms

2017 ◽  
Vol 8 (2) ◽  
pp. 240-247 ◽  
Author(s):  
Jianguo Zhao ◽  
Junliang Wu
Keyword(s):  
Operator Inequalities ◽  
Unitarily Invariant Norms

scholarly journals Operator Inequalities Implying Similarity to a Contraction

2018 ◽  
Vol 13 (3) ◽  
pp. 1325-1360
Author(s):  
Glenier Bello-Burguet ◽  
Dmitry Yakubovich
Keyword(s):  
Operator Inequalities

scholarly journals On quantum quasi-relative entropy

2019 ◽  
Vol 31 (07) ◽  
pp. 1950022
Author(s):  
Anna Vershynina
Keyword(s):  
Relative Entropy ◽  
Logarithmic Function ◽  
Operator Inequalities ◽  
Operator Convex Function ◽  
Strong Subadditivity ◽  
Entropy Formula ◽  
Quantum Relative Entropy ◽  
Skew Information ◽  
Explicit Bounds ◽  
Joint Convexity

We consider a quantum quasi-relative entropy [Formula: see text] for an operator [Formula: see text] and an operator convex function [Formula: see text]. We show how to obtain the error bounds for the monotonicity and joint convexity inequalities from the recent results for the [Formula: see text]-divergences (i.e. [Formula: see text]). We also provide an error term for a class of operator inequalities, that generalizes operator strong subadditivity inequality. We apply those results to demonstrate explicit bounds for the logarithmic function, that leads to the quantum relative entropy, and the power function, which gives, in particular, a Wigner–Yanase–Dyson skew information. In particular, we provide the remainder terms for the strong subadditivity inequality, operator strong subadditivity inequality, WYD-type inequalities, and the Cauchy–Schwartz inequality.

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