On $J$ -frames related to maximal definite subspaces

Abstract

We propose a definition of frames in Krein spaces which generalizes the concept of J-frames defined relatively recently by Giribet, Maestripieri, Martínez-Pería, and Massey. The difference consists in the fact that a J-frame is related to maximal definite subspaces M± which are not assumed to be uniformly definite. The latter allows us to extend the set of J-frames. In particular, some J-orthogonal Schauder bases can be interpreted as J-frames.