Duality for frames in Krein spaces. Issue 5 (3rd January 2018)

• Record Type: Journal Article
• Authors: Giribet, Juan Ignacio; Maestripieri, Alejandra; Martínez Pería, Francisco
• Is Part Of: Mathematische Nachrichten. Volume 291:Issue 5/6(2018)
• Page Start: 879
• Page End: 896
• Publication Date: 2018-01-03
• Subjects: Frames -- Krein spaces -- signal processing -- Primary: 42C15; Secondary: 46C20 -- 47B50; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201700149
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract: 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.