Advances in Operator Theory

Tsallis relative operator entropy with negative parameters

Jun Ichi Fujii and Yuki Seo

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Tsallis relative operator entropy was firstly formulated by Fujii and Kamei as an operator version of Uhlmann's relative entropy. Afterwards, Yanagi, Kuriyama and Furuichi reformulated Tsallis relative operator entropy as an operator version of Tsallis relative entropy. In this paper, we define Tsallis relative operator entropy with negative parameters of (non-invertible) positive operators on a Hilbert space and show some properties.

Article information

Adv. Oper. Theory, Volume 1, Number 2 (2016), 219-235.

Received: 26 October 2016
Accepted: 18 December 2016
First available in Project Euclid: 4 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A63: Operator inequalities
Secondary: 47A64: Operator means, shorted operators, etc.

Tsallis relative operator entropy positive operator operator geometric mean


Fujii, Jun Ichi; Seo, Yuki. Tsallis relative operator entropy with negative parameters. Adv. Oper. Theory 1 (2016), no. 2, 219--235. doi:10.22034/aot.1610.1038.

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