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Generalized Shannon inequalities based on Tsallis relative operator entropy

Kenjiro Yanagi·Ken Kuriyama·Shigeru Furuichi
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Abstract

Tsallis relative operator entropy is defined and then its properties are given. Shannon inequality and its reverse one in Hilbert space operators derived by T.Furuta \cite{Fu:par} are extended in terms of the parameter of the Tsallis relative operator entropy. Moreover the generalized Tsallis relative operator entropy is introduced and then several operator inequalities are derived.

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Kenjiro Yanagi, Ken Kuriyama, Shigeru Furuichi. 2005-04-05. Generalized Shannon inequalities based on Tsallis relative operator entropy. https://arxiv.org/abs/math/0406137

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