论文标题
JB-Elgebras中的相对操作员熵和Tsallis相对操作员熵
Relative operator entropies and Tsallis relative operator entropies in JB-algebras
论文作者
论文摘要
我们在JB-Elgebras的设置中启动了相对操作员熵和Tsallis相对操作员熵的研究。我们建立了它们的基本属性，并扩展了对相对操作员熵和TSALLIS相对操作员熵的操作员不平等。此外，我们改善了相对运算符$（α，β）$ - 熵的下限和上限，在Nikoufar [18，20]设置的Hilbert太空运营商中建立的JB-Elgebras设置。尽管我们采用与希尔伯特太空运营商的经典环境相同的符号，但JB-Algebras环境中的不平等具有不同的含义，其证明需要在JB-Algebras中采用技术。
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 [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.
