Hilbert-Schauder frame operators

Abstract

We introduce a new concept of frame operators for Banach spaces we call a HilbertSchauder 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 p and Lp -spaces with 1 < p 2 . Finally, we give a new isomorphic characterization of Hilbert spaces. Mathematics subject classification (2010): Primary 46B15, 46B28, 46B45, 47B38; Secondary 47A20.