On frames for Krein spaces

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• 作者：J.I. Giribet^a ; ^b ; ^{jgiribet@fi.uba.ar} ; A. Maestripieri^a ; ^b ; ^{amaestri@fi.uba.ar} ; F. Martí ; nez Perí ; a^c ; ^b ; ^{francisco@mate.unlp.edu.ar} ; P.G. Massey^c ; ^b ; ^{massey@mate.unlp.edu.ar}
• 关键词：Krein spaces ; Frames ; Uniformly J-definite subspaces
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 期刊代码：76_0022247x
• 类别：mt
• 出版时间：1 September, 2012
• 卷：393
• 期：1
• 页码：122-137
• 文件大小：317 K

摘要

A definition of frames for Krein spaces is proposed, which extends the notion of -orthonormal bases of Krein spaces. A -frame for a Krein space is in particular a frame for in the Hilbert space sense. But it is also compatible with the indefinite inner product , meaning that it determines a pair of maximal uniformly -definite subspaces, an analogue to the maximal dual pair associated to a -orthonormal basis.

Also, each -frame induces an indefinite reconstruction formula for the vectors in , which resembles the one given by a -orthonormal basis.