We propose a definition of frames in Krein spaces which generalizes the concept of -frames defined relatively recently by Giribet, Maestripieri, Martínez-Pería, and Massey. The difference consists in the fact that a -frame is related to maximal definite subspaces which are not assumed to be uniformly definite. The latter allows us to extend the set of -frames. In particular, some -orthogonal Schauder bases can be interpreted as -frames.
"On -frames related to maximal definite subspaces." Ann. Funct. Anal. 10 (1) 106 - 121, February 2019. https://doi.org/10.1215/20088752-2018-0012