Schur complements in Krein spaces

Abstract

The aim of this work is to generalize the notions of Schur complements and shorted operators to Krein spaces. Given a (bounded) J-selfadjoint operator A (with the unique factorization property) acting on a Krein space H and a suitable closed subspace S of H, the Schur complement A/[s]of A to S is defined. The basic properties of A/ are developed and different characterizations are given, most of them resembling those of the shorted of (bounded) positive operators on a Hilbert space.