Advances in Operator Theory

Tsallis relative operator entropy with negative parameters

Jun Ichi Fujii and Yuki Seo

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512431398

Digital Object Identifier
doi:10.22034/aot.1610.1038

Mathematical Reviews number (MathSciNet)
MR3723622

Zentralblatt MATH identifier
1368.47017

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

Keywords
Tsallis relative operator entropy positive operator operator geometric mean

Citation

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. https://projecteuclid.org/euclid.aot/1512431398


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