Perturbation of p-approximate Schauder frames for separable Banach spaces

TL;DR

This paper extends the Paley-Wiener theorem to p-approximate Schauder frames in separable Banach spaces, connecting it with existing theorems for Hilbert space frames.

Contribution

It introduces a Paley-Wiener theorem for p-approximate Schauder frames, broadening the theoretical framework for frames in Banach spaces.

Findings

Paley-Wiener theorem derived for p-approximate Schauder frames

Results recover classical Paley-Wiener theorem for Hilbert space frames

Provides new insights into the structure of frames in Banach spaces

Abstract

Paley-Wiener theorem for frames for Hilbert spaces, Banach frames, Schauder frames and atomic decompositions for Banach spaces are known. In this paper, we derive Paley-Wiener theorem for p-approximate Schauder frames for separable Banach spaces. We show that our results give Paley-Wiener theorem for frames for Hilbert spaces.