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A $J$-frame for a Krein space $\mathcal{H}$ is in particular a frame for$\mathcal{H}$ (in the Hilbert space sense). But it is also compatible with theindefinite inner-product of $\mathcal{H}$, meaning that it determines a pair ofmaximal uniformly definite subspaces, an analogue to the maximal dual pairassociated to an orthonormal basis in a Krein space. This work is devoted tostudy duality for $J$-frames in Krein spaces. Also, tight and Parseval$J$-frames are defined and characterized.

Duality for Frames in Krein Spaces