Geodesic
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
Raïssouli, Mustapha 1 ,  2   ; Moslehian, Mohammad Sal 3   ; Furuichi, Shigeru 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, Tome 355 (2017) no. 6, pp. 687-693 Cet article a éte moissonné depuis la source Numdam

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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.

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.

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DOI : 10.1016/j.crma.2017.05.005

Raïssouli, Mustapha  1 , 2   ; Moslehian, Mohammad Sal  3   ; Furuichi, Shigeru  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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     title = {Relative entropy and {Tsallis} entropy of two accretive operators},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {687--693},
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Raïssouli, Mustapha; Moslehian, Mohammad Sal; Furuichi, Shigeru. Relative entropy and Tsallis entropy of two accretive operators. Comptes Rendus. Mathématique, Tome 355 (2017) no. 6, pp. 687-693. doi: 10.1016/j.crma.2017.05.005

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