Relative entropy and Tsallis entropy of two accretive operators

Mustapha Raïssouli; Mohammad Sal Moslehian; Shigeru Furuichi

doi:10.1016/j.crma.2017.05.005

Functional analysis

Relative entropy and Tsallis entropy of two accretive operators
[Entropie relative et entropie de Tsallis de deux opérateurs accrétifs]

Présenté par : the Editorial Board

Mustapha Raïssouli ^1,² ; Mohammad Sal Moslehian ³ ; Shigeru Furuichi ⁴

¹ Department of Mathematics, Science Faculty, Taibah University, Al Madinah Al Munawwarah, P.O. Box 30097, Zip Code 41477, Saudi Arabia
² Department of Mathematics, Faculty of Science, Moulay Ismail University, Meknes, Morocco
³ Department of Pure Mathematics, P.O. Box 1159, Ferdowsi University of Mashhad, Mashhad 91775, Iran
⁴ Department of Information Science, College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajyousui, Setagaya-ku, Tokyo, 156-8550, Japan

Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 687-693.

Résumé
Abstract

Soient A et B deux opérateurs accrétifs. Nous introduisons d'abord une moyenne géométrique pondérée de A et de B et nous en étudions certaines propriétés. Nous définissons ensuite l'entropie relative ainsi que l'entropie de Tsallis de A et de B. Ces définitions et les résultats obtenus étendent ceux déjà énoncés dans la littérature pour les opérateurs inversibles positifs.

Let A and B be two accretive operators. We first introduce the weighted geometric mean of A and B together with some related properties. Afterwards, we define the relative entropy as well as the Tsallis entropy of A and B. The present definitions and their related results extend those already introduced in the literature for positive invertible operators.

Reçu le : 2017-03-23
Accepté le : 2017-05-18
Publié le : 2017-05-31

DOI : 10.1016/j.crma.2017.05.005

Affiliations des auteurs :

Mustapha Raïssouli ^{1, 2} ; Mohammad Sal Moslehian ³ ; Shigeru Furuichi ⁴

¹ Department of Mathematics, Science Faculty, Taibah University, Al Madinah Al Munawwarah, P.O. Box 30097, Zip Code 41477, Saudi Arabia
² Department of Mathematics, Faculty of Science, Moulay Ismail University, Meknes, Morocco
³ Department of Pure Mathematics, P.O. Box 1159, Ferdowsi University of Mashhad, Mashhad 91775, Iran
⁴ Department of Information Science, College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajyousui, Setagaya-ku, Tokyo, 156-8550, Japan

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     author = {Mustapha Ra{\"\i}ssouli and Mohammad Sal Moslehian and Shigeru Furuichi},
     title = {Relative entropy and {Tsallis} entropy of two accretive operators},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {687--693},
     publisher = {Elsevier},
     volume = {355},
     number = {6},
     year = {2017},
     doi = {10.1016/j.crma.2017.05.005},
     language = {en},
}

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Mustapha Raïssouli; Mohammad Sal Moslehian; Shigeru Furuichi. Relative entropy and Tsallis entropy of two accretive operators. Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 687-693. doi : 10.1016/j.crma.2017.05.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.05.005/

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