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- W2997763727 abstract "This paper intends to give some new estimates for Tsallis relative operator entropy ${{T}_{v}}left( A|B right)=frac{A{{natural}_{v}}B-A}{v}$. Let $A$ and $B$ be two positive invertible operators with the spectra contained in the interval $J subset (0,infty)$. We prove for any $vin left[ -1,0 right)cup left( 0,1 right]$, $$ (ln_v t)A+left( A{{natural}_{v}}B+tA{{natural}_{v-1}}B right)le {{T}_{v}}left( A|B right) le (ln_v s)A+{{s}^{v-1}}left( B-sA right) $$ where $s,tin J$. 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." @default.
- W2997763727 created "2020-01-10" @default.
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- W2997763727 date "2020-01-05" @default.
- W2997763727 modified "2023-09-26" @default.
- W2997763727 title "Some remarks on Tsallis relative operator entropy" @default.
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- W2997763727 doi "https://doi.org/10.48550/arxiv.2001.01342" @default.
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