On frames for Krein spaces

Abstract

A definition of frames for Krein spaces is proposed, which extends the notion of J-orthonormal bases of 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 [ , ], meaning that it determines a pair of maximal uniformly J-definite subspaces, 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 H, which resembles the one given by a J-orthonormal basis.