## Annals of Functional Analysis

### 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.

#### Article information

Source
Ann. Funct. Anal., Volume 10, Number 1 (2019), 106-121.

Dates
Accepted: 14 May 2018
First available in Project Euclid: 16 January 2019

https://projecteuclid.org/euclid.afa/1547629227

Digital Object Identifier
doi:10.1215/20088752-2018-0012

Mathematical Reviews number (MathSciNet)
MR3899960

Zentralblatt MATH identifier
07045489

#### Citation

Kamuda, Alan; Kuzhel, Sergii. On $J$ -frames related to maximal definite subspaces. Ann. Funct. Anal. 10 (2019), no. 1, 106--121. doi:10.1215/20088752-2018-0012. https://projecteuclid.org/euclid.afa/1547629227

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