HILBERT-SCHAUDER FRAME OPERATORS

We introduce a new concept of frame operators for Banach spaces we call a Hilbert-Schauder frame operator. This is a hybird between standard frame theory for Hilbert spaces and Schauder frame theory for Banach spaces. Most of our results involve basic structure properties of the Hilbert-Schauder frame operator. Examples of Hilbert-Schauder frames include standard Hilbert frames and classical bases of l(p) and L-p-spaces with 1 < p <= 2. Finally, we give a new isomorphic characterization of Hilbert spaces.