2020/02/05 by Tarcsay, Zsigmond, Titkos, Tamás
#28A12 #46K10 #47B65 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2002.01714
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.