Annals of Functional Analysis

On J-frames related to maximal definite subspaces

Alan Kamuda and Sergii Kuzhel

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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.

Article information

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

Received: 6 January 2018
Accepted: 14 May 2018
First available in Project Euclid: 16 January 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B50: Operators on spaces with an indefinite metric [See also 46C50]
Secondary: 46C20: Spaces with indefinite inner product (Krein spaces, Pontryagin spaces, etc.) [See also 47B50]

Krein space frame J-orthogonal sequence Schauder basis


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.

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