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Register a new userRelative operator entropies and Tsallis relative operator entropies in JB-algebras
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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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In this paper, we investigate the relative operator entropies in the more general settings of C*-algebras, real C*-algebras and JC-algebras. We show that all the operator inequalities on relative operator entropies still hold in these broader settings. In addition, we improve the lower and upper bounds of the relative operator $(alpha, beta)$-entropy established by Nikoufar which refined the bounds for the relative operator entropy obtained by Fujii and Kamei.
In this paper, the notion of operator means in the setting of JB-algebras is introduced and their properties are studied. Many identities and inequalities are established, most of them have origins from operators on Hilbert space but they have different forms and connotations, and their proofs require techniques in JB-algebras.
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