We consider G-projectors (orthogonal projections) defined on an indefinite inner product space, and derive in a systematic way the indefinite counterparts of a number of useful results known to hold for ordinary projectors in Hilbert space. Some of the topological considerations encountered in the literature are avoided here, and several results are 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 given for a nondecreasing sequence of G-contractive G-projectors. We also prove a result characterizing G-projectors within the class of idempotents, generalizing the corresponding result in Hilbert space.
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics