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2015 On an Analogue of $ABA$ when the Operator Variables $A$ and $B$ are Convex Functionals
Mustapha Raïssouli
Banach J. Math. Anal. 9(1): 235-242 (2015). DOI: 10.15352/bjma/09-1-17

Abstract

The operator-product $ABA$ appears in many mathematical contexts, such as in algebraic Riccati equation, in operator entropy and in operator-mean theory. The purpose of the present paper is to investigate a reasonable analogue of $ABA$ when the positive linear operators $A$ and $B$ are convex functionals. As consequence, the square of a convex functional extending $A^2$ is provided as well.

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Mustapha Raïssouli. "On an Analogue of $ABA$ when the Operator Variables $A$ and $B$ are Convex Functionals." Banach J. Math. Anal. 9 (1) 235 - 242, 2015. https://doi.org/10.15352/bjma/09-1-17

Information

Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1310.47118
MathSciNet: MR3296097
Digital Object Identifier: 10.15352/bjma/09-1-17

Subjects:
Primary: 46N10
Secondary: ‎39B62 , 46A20 , 47N10‎ , 52A41

Keywords: Fenchel duality , functional inequalities , generalized inner product , point-wise convexity , positive linear operator

Rights: Copyright © 2015 Tusi Mathematical Research Group

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