2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77759We develope a local theory for frames on finite dimensional Hilbert spaces. In particular, a bounded frame on a finite dimensional Hilbert space contains a subset 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 which contains a subset which is a Schauder basis for H but does not contain any subset which is a Riesz basis for H.15 pages; to appear: Illinois J. MathFunctional Analysis46C05; 46B07text