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.
"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