Expansion of weak reconstruction sequences to approximate Schauder frames for Banach spaces

Abstract

It is known in Hilbert space frame theory that a Bessel sequence can be expanded to a frame. Contrary to Hilbert space situation, using a result of Casazza and Christensen, we show that there are Banach spaces and weak reconstruction sequences which cannot be expanded to approximate Schauder frames. We characterize Banach spaces in which one can expand weak reconstruction sequences to approximate Schauder frames. © 2022 World Scientific Publishing Company.