Alan Kamuda, Sergii Kuzhel. Source: Annals of Functional Analysis, Volume 10, Number 1, 106--121.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.