On frames for Krein spaces

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