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June 2022 Relative operator entropies and Tsallis relative operator entropies in JB-algebras
Shuzhou Wang, Zhenhua Wang
Rocky Mountain J. Math. 52(3): 1073-1087 (June 2022). DOI: 10.1216/rmj.2022.52.1073

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 (α,β)-entropy in the setting of JB-algebras that were established in Hilbert space operators setting by Nikoufar (2014; 2020). 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 require techniques in JB-algebras.

Citation

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Shuzhou Wang. Zhenhua Wang. "Relative operator entropies and Tsallis relative operator entropies in JB-algebras." Rocky Mountain J. Math. 52 (3) 1073 - 1087, June 2022. https://doi.org/10.1216/rmj.2022.52.1073

Information

Received: 29 July 2021; Accepted: 24 September 2021; Published: June 2022
First available in Project Euclid: 16 June 2022

Digital Object Identifier: 10.1216/rmj.2022.52.1073

Subjects:
Primary: 46H70 , 47A56 , 47A60 , 47A63 , 94A17
Secondary: 17C65 , 46N50 , 81P45 , 81R15

Keywords: JB-algebras , Operator inequalities , relative operator entropies , Tsallis relative operator entropies

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 3 • June 2022
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