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Schur complements of selfadjoint Krein space operators (1809.01695v4)
Published 5 Sep 2018 in math.FA
Abstract: Given a bounded selfadjoint operator W on a Krein space H and a closed subspace S of H, the Schur complement of W to S is defined under the hypothesis of weak complementability. A variational characterization of the Schur complement is given and the set of selfadjoint operators W admitting a Schur complement with these variational properties is shown to coincide with the set of S-weakly complementable selfadjoint operators.