Operators on anti-dual pairs: Generalized Schur complement

Published 5 Feb 2020 in math.FA | (2002.01714v1)

Abstract: The goal of this paper is to develop the theory of Schur complementation in the context of operators acting on anti-dual pairs. As a byproduct, we obtain a natural generalization of the parallel sum and parallel difference, as well as the Lebesgue-type decomposition. To demonstrate how this operator approach works in application, we derive the corresponding results for operators acting on rigged Hilbert spaces, and for representable functionals of ${}^{{*}$-algebras.}