  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 approximate
Bessel sequences which can not be expanded to approximate Schauder frames. We
characterize Banach spaces in which one can expand approximate Bessel sequences
to approximate Schauder frames.
