Refined operator inequalities for relative operator entropies

2020/12/22 by Wang, Shuzhou, Wang, Zhenhua
#17C65 #46L70 #47A56 #47A60(Primary) 46N50 #47A63 #47L30 #81P45(Secondary) #81R15 #94A17 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2012.12399

Abstract

In this paper, we investigate the relative operator entropies in the more general settings of C*-algebras, real C*-algebras and JC-algebras. We show that all the operator inequalities on relative operator entropies still hold in these broader settings. In addition, we improve the lower and upper bounds of the relative operator (α, β)-entropy established by Nikoufar which refined the bounds for the relative operator entropy obtained by Fujii and Kamei.

Related

• Relative operator entropies and Tsallis relative operator entropies in JB-algebras
• Precise estimates of bounds on relative operator entropies
• Inequalities for relative operator entropies and operator means
• Some remarks on Tsallis relative operator entropy
• Generalized Shannon inequalities based on Tsallis relative operator entropy