We develope a local theory for frames on finite dimensional Hilbert spaces.In particular, a bounded frame on a finite dimensional Hilbert space contains asubset which is a good Riesz basis for a percentage (arbitrarily close to one)of the space. We also construct a normalized frame for a Hilbert space whichcontains a subset which is a Schauder basis for H but does not contain anysubset which is a Riesz basis for H.
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