  We prove that a Schauder frame for any separable Banach space is shrinking if
and only if it has an associated space with a shrinking basis, and that a
Schauder frame for any separable Banach space is shrinking and boundedly
complete if and only if it has a reflexive associated space. To obtain these
results, we prove that the upper and lower estimate theorems for finite
dimensional decompositions of Banach spaces can be extended and modified to
Schauder frames. We show as well that if a separable infinite dimensional
Banach space has a Schauder frame, then it also has a Schauder frame which is
not shrinking.
