Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to c0

Abstract

We prove that a Hilbert space frame {fi}i ∈ I, contains a Riesz basis if every subfamily {fi}i ∈ J, J ⊆ 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 c0. This result immediately leads to an improvement of a recent theorem of Holub concerning frames consisting of a Riesz basis plus finitely many elements © 1996 Academic Press, Inc.