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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153004We prove that a Hilbert space frame $\fti$ contains a Riesz basis if every subfamily $\ftj , J \subseteq I ,$ 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.Functional Analysis42CHilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to $c_0$text