Normal projections in Krein spaces

Abstract

Given a complex Krein space H with fundamental symmetry J, the aim of this note is to characterize the set of J-normal projections Q = {Q ∈ L(H): Q2 and Q#Q = QQ#}. The ranges of the projections in Q are exactly those subspaces of H which are pseudo-regular. For a fixed pseudo-regular subspace S, there are infinitely many J-normal projections onto it, unless S is regular. Therefore, most of the material herein is devoted to parametrizing the set of J-normal projections onto a fixed pseudo-regular subspace S.