Hilbert-Schauder Frame Operators

Abstract

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 ${\ell }_p$ and $L^p$-spaces with $1<p\le 2$. Finally, we give a new isomorphic characterization of Hilbert spaces.

9 pages, to appear in Operators and Matrices

References in corpus (2)

• A characterization of Schauder frames which are near-Schauder bases
• Moving Parseval frames for vector bundles