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- W1736144695 abstract "Let $mathbb{A}=(A_1,cdots,A_n)$ and $mathbb{B}=(B_1,cdots,B_n)$ be operator distributions, that is, $A_i, B_i>0$ $(1leq i leq n)$ and $sum_{i=1}^n A_i =sum_{i=1}^n B_i =I$. We give a new relative operator entropy of two operator distributions as follows: For $t,s in mathbb{R} setminus {0}$, [ K_{t,s}(mathbb{A}|mathbb{B}) equiv dfrac{(sum_{i=1}^n A_i sharp_{t} B_i)^s -I}{ts}, ] where ( A sharp_{t} B = A^{frac12} (A^{frac{-1}2} B A^{frac{-1}2})^{t} A^{frac12}. ) This includes relative operator entropy $S(mathbb{A}|mathbb{B})$, Rényi relative operator entropy $I_{t}(mathbb{A}|mathbb{B})$ and Tsallis relative operator entropy $T_{t}(mathbb{A}|mathbb{B})$. In this paper, firstly, we discuss fundamental properties of $K_{t,s}(mathbb{A}|mathbb{B})$. Secondly, we obtain Shannon type operator inequalities by using $K_{t,s}(mathbb{A}|mathbb{B})$, which include previous results by Furuta, Yanagi--Kuriyama--Furuichi and ourselves." @default.
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- W1736144695 date "2015-01-01" @default.
- W1736144695 modified "2023-09-27" @default.
- W1736144695 title "Shannon type inequalities of a relative operator entropy including Tsallis and Rényi ones" @default.
- W1736144695 doi "https://doi.org/10.15352/afa/06-4-289" @default.
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