Some remarks on Tsallis relative operator entropy

2020/01/06 by Shigeru Furuichi, Hamid Reza Moradi, Furuichi, Shigeru +1
Mathematics · Medicine · #47A60 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Numerical methods in inverse problems #Pregnancy-related medical research #Primary 47A63 #Secondary 46L05

paper · pdf · doi:10.48550/arxiv.2001.01342

openalex publication_date 2020/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper intends to give some new estimates for Tsallis relative operator entropy T_v( A|B )=\fracA\natural_vB-Av. Let A and B be two positive invertible operators with the spectra contained in the interval J ⊂ (0,∞). We prove for any v∈ [ -1,0 )∪ ( 0,1 ], (ln_v t)A+( A\natural_vB+tA\natural_v-1B )≤ T_v( A|B ) ≤ (ln_v s)A+s^v-1( B-sA ) where s,t∈ J. Especially, the upper bound for Tsallis relative operator entropy is a non-trivial new result. Meanwhile, some related and new results are also established. In particular, the monotonicity for Tsallis relative operator entropy is improved. Furthermore, we introduce the exponential type relative operator entropies which are special cases of the perspective and we give inequalities among them and usual relative operator entropies.

Citations

• Some inequalities for interpolational operator means

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