Local Theory of Frames and Schauder Bases for Hilbert Space
نویسنده
چکیده
We develope a local theory for frames on finite dimensional Hilbert spaces. We show that for every frame (fi) m i=1 for an n-dimensional Hilbert space, and for every ǫ > 0, there is a subset I ⊂ {1, 2, . . . ,m} with |I| ≥ (1 − ǫ)n so that (fi)i∈I is a Riesz basis for its span with Riesz basis constant a function of ǫ, the frame bounds, and (‖fi‖) m i=1 , but independent of m and n. We also construct an example of a normalized frame for a Hilbert space H which contains a subset which forms a Schauder basis for H, but contains no subset which is a Riesz basis for H. We give examples to show that all of our results are best possible, and that all parameters are necessary.
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