Tsallis relative operator entropy with negative parameters. (English) Zbl 1368.47017

Fujii, Jun Ichi; Seo, Yuki

Adv. Oper. Theory 1, No. 2, 219-235 (2016).

Summary: Tsallis relative operator entropy was firstly formulated by the first author and E. Kamei [Math. Japon. 34, No. 3, 341–348 (1989; Zbl 0699.46048); Math. Japon. 34, No. 4, 541–547 (1989; Zbl 0695.47013)] as an operator version of Uhlmann’s relative entropy. Afterwards, K. Yanagi et al. [Linear Algebra Appl. 394, 109–118 (2005; Zbl 1059.47018)] 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.

MSC:

47A63	Linear operator inequalities
47A64	Operator means involving linear operators, shorted linear operators, etc.
94A17	Measures of information, entropy

Keywords:

Tsallis relative operator entropy; positive operator; operator geometric mean

Citations:

Zbl 0699.46048; Zbl 0695.47013; Zbl 1059.47018