Existence of Parseval oblique duals of a frame sequence

We present a collection of necessary and sufficient conditions for the existence of a Parseval oblique dual (in an appropriate subspace) of a frame sequence. This result extends the previous results by Han and Larson, Antezana et al. and Han. Our proof shows that the problem is closely related with that of extending an operator with norm less than or equal to 1 to an isometry on a subspace.