This is an announcement for the paper "Hilbert-Schauder frame operators" by Rui Liu.

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.

Archive classification: math.FA math.CA math.OA

Mathematics Subject Classification: 46B, 47B, 47A

Remarks: 9 pages, to appear in Operators and Matrices

Submitted from: ruiliu@nankai.edu.cn

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1206.6146

or

http://arXiv.org/abs/1206.6146