ON PROJECTIONS IN A SPACE WITH AN INDEFINITE METRIC

We consider G-projectors (orthogonal projections) defined on an indefi nite inner product space, and derive in a systematic way the indefinit e counterparts of a number of useful results known to hold for ordinar y projectors in Hilbert space. Some of the topological considerations encountered in the literature are avoided here, and several results ar e obtained using quite elementary matrix-type arguments. In particular , the relation between G-projectors and contractions in an indefinite inner product space is studied. For example, a convergence result is g iven for a nondecreasing sequence of G-contractive G-projectors. We al so prove a result characterizing G-projectors within the class of idem potents, generalizing the corresponding result in Hilbert space.