Relative operator entropies and Tsallis relative operator entropies in JB-algebras

• URL: http://arxiv.org/abs/2012.13480v2
• Date: Thu, 29 Jul 2021 18:31:39 GMT
• Title: Relative operator entropies and Tsallis relative operator entropies in JB-algebras
• Authors: Shuzhou Wang and Zhenhua Wang
• Abstract summary: We study relative operator entropies and Tsallis relative operator entropies in the setting of JB-algebras. We extend the operator inequalities on relative operator entropies and Tsallis relative operator entropies to this setting.
• Score: 2.40740109080792
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We initiate the study of relative operator entropies and Tsallis relative operator entropies in the setting of JB-algebras. We establish their basic properties and extend the operator inequalities on relative operator entropies and Tsallis relative operator entropies to this setting. In addition, we improve the lower and upper bounds of the relative operator $(\alpha, \beta)$-entropy in the setting of JB-algebras that were established in Hilbert space operators setting by Nikoufar [18, 20]. Though we employ the same notation as in the classical setting of Hilbert space operators, the inequalities in the setting of JB-algebras have different connotations and their proofs requires techniques in JB-algebras.

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