Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to c(0)

We prove that a Hilbert space frame {f(i)}(i is an element of I) contains a Riesz basis if every subfamily {f(i)}(i is an element of J), J subset of or equal to I is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic to c(0). This result immediately leads to an improvement of a recent theorem of Holub concerning frames consisting of a Riesz basis plus finitely many elements. (C) 1996 Academic Press, Inc.