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 ${\mathcal{M}}_{\pm }$ 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.