On complementable operators in the sense of T. Ando

Abstract

Consider an operator A:H→K between Hilbert spaces and closed subspaces S⊂H and T⊂K. If there exist projections E on H and F on K such that R(E)=S, R(F)=T and AE=F⁎A then A is called (S,T)-complementable. The origin of this notion comes from the idea of T. Ando of defining Schur complements in terms of operators. In this paper we present some characterizations of these triples (A,S,T) and applications to bilateral Schur complements and generalized Wiener-Hopf operators.