Approximately Dual p-Approximate Schauder Frames

TL;DR

This paper introduces approximately dual frames for a specific class of approximate Schauder frames in Banach spaces, providing a complete characterization and analyzing their stability under perturbations.

Contribution

It extends the concept of approximately dual frames from Hilbert spaces to Banach spaces and develops foundational theory for this class.

Findings

Complete characterization of approximately dual frames in Banach spaces

Analysis of perturbation stability for these frames

Extension of dual frame concepts beyond Hilbert spaces

Abstract

Difficulty in the construction of dual frames for a given Hilbert space led to the introduction of approximately dual frames in Hilbert spaces by Christensen and Laugesen. It becomes even more difficult in Banach spaces to construct duals. For this purpose, we introduce approximately dual frames for a class of approximate Schauder frames for Banach spaces and develop basic theory. Approximate duals for this subclass is completely characterized and its perturbation is also studied.