Pseudo- Riesz Bases

TL;DR

This paper introduces a generalized concept of near-Riesz bases that includes non-frame sequences, expanding the class of bases with desirable properties and establishing key perturbation results.

Contribution

It generalizes near-Riesz bases to include non-frame sequences, maintaining key properties and providing foundational perturbation theorems.

Findings

Broader class of sequences retains Riesz-like properties

Fundamental perturbation results established

Includes sequences not necessarily frames

Abstract

In~\cite{holub1994bases} Holub introduced the concept of near-Riesz bases, as frames that can be considered Riesz bases for computational purposes or that exhibit certain desirable properties of Riesz bases. In this paper, we introduce a generalization of near-Riesz bases that includes sequences which are not necessarily frames. We demonstrate that this broader class of sequences retains many of the desirable properties of near-Riesz bases and establish fundamental perturbation results for this new class.