  We introduce the notion of a continuous Schauder frame for a Banach space.
This is both a generalization of continuous frames and coherent states for
Hilbert spaces and a generalization of unconditional Schauder frames for Banach
spaces. As a natural example, we prove that any wavelet for $L_p(\R)$ with
$1<p<\infty$ generates a continuous wavelet Schauder frame. Furthermore, we
generalize the properties shrinking and boundedly complete to the continuous
Schauder frame setting, and prove that many of the fundamental James theorems
still hold in this general context.
