Oblique projections and frames

Abstract

We characterize those frames on a Hilbert space H which can be represented as the image of an orthonormal basis by an oblique projection defined on an extension K of H. We show that all frames with infinite excess, and frame bounds 1 ≤ A ≤ B,are of this type. This gives a generalization of a result of Han and Larson which only holds for normalized tight frames.