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G-frames and G-Riesz Bases

Wenchang Sun
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Abstract

G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural generalizations of frames and provide more choices on analyzing functions from frame expansion coefficients. We give characterizations of g-frames and prove that g-frames share many useful properties with frames. We also give generalized version of Riesz bases and orthonormal bases. As an application, we get atomic resolutions for bounded linear operators.

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Wenchang Sun. 2005-08-05. G-frames and G-Riesz Bases. https://arxiv.org/abs/math/0508104

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