On a family of frames for Krein spaces
arXiv:1112.1632
Abstract
A definition of frames for Krein spaces is proposed, which extends the notion of -orthonormal basis of Krein spaces. A -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 -definite subspaces with different positivity, an analogue to the maximal dual pair associated to a -orthonormal basis. Also, each -frame induces an indefinite reconstruction formula for the vectors in $\HH$, which resembles the one given by a -orthonormal basis.