Duality for frames in Krein spaces

A J‐frame for a Krein space H is in particular a frame for H (in the Hilbert space sense). But it is also compatible with the indefinite inner‐product of H, meaning that it determines a pair of maximal uniformly definite subspaces, an analogue to the maximal dual pair associated with an orthonormal...

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Bibliographic Details
Published in:	Mathematische Nachrichten Vol. 291; no. 5-6; pp. 879 - 896
Main Authors:	Giribet, Juan Ignacio, Maestripieri, Alejandra, Martínez Pería, Francisco
Format:	Journal Article
Language:	English
Published:	Weinheim Wiley Subscription Services, Inc 01-04-2018
Subjects:	47B50 Frames Hilbert space Krein spaces Primary: 42C15; Secondary: 46C20 signal processing Subspaces
Online Access:	Get full text
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Summary:	A J‐frame for a Krein space H is in particular a frame for H (in the Hilbert space sense). But it is also compatible with the indefinite inner‐product of H, meaning that it determines a pair of maximal uniformly definite subspaces, an analogue to the maximal dual pair associated with an orthonormal basis in a Krein space. This work is devoted to study duality for J‐frames in Krein spaces. Also, tight and Parseval J‐frames are defined and characterized.
ISSN:	0025-584X 1522-2616
DOI:	10.1002/mana.201700149