On frames for Krein spaces

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