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arXiv · 1112.1632

On a family of frames for Krein spaces

J. I. Giribet·A. Maestripieri·F. Martínez Pería·P. Massey
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Abstract

A definition of frames for Krein spaces is proposed, which extends the notion of $J$-orthonormal basis of Krein spaces. A $J$-frame for a Krein space $(\HH, \K{\,}{\,})$ is in particular a frame for $\HH$ in the Hilbert space sense. But it is also compatible with the indefinite inner product $\K{\,}{\,}$, meaning that it determines a pair of maximal uniformly $J$-definite subspaces with different positivity, an analogue to the maximal dual pair associated to a $J$-orthonormal basis. Also, each $J$-frame induces an indefinite reconstruction formula for the vectors in $\HH$, which resembles the one given by a $J$-orthonormal basis.

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J. I. Giribet, A. Maestripieri, F. Martínez Pería, P. Massey. 2011-12-07. On a family of frames for Krein spaces. https://arxiv.org/abs/1112.1632

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