Perturbation of frames in Banach spaces

TL;DR

This paper investigates how various frame-like structures in Banach spaces, such as X_d-Bessel sequences and Banach frames, are affected by perturbations, establishing conditions under which these structures remain stable or equivalent.

Contribution

It provides new insights into the stability and equivalence of perturbations for frames and bases in Banach spaces, extending existing theories.

Findings

Identifies conditions for perturbation stability of Banach frames.

Establishes equivalence between different perturbation conditions.

Analyzes the impact of perturbations on atomic decompositions and Riesz bases.

Abstract

In this paper we consider perturbation of X_d-Bessel sequences, X_d-frames, Banach frames, atomic decompositions and X_d-Riesz bases in separable Banach spaces. Equivalence between some perturbation conditions is investigated.