On perturbations of woven pairs of frames

TL;DR

This paper investigates how small perturbations affect woven pairs of frames in Hilbert spaces, providing new results that extend existing knowledge and exploring conditions similar to Riesz frames.

Contribution

It offers new theorems on perturbations of frames to maintain weaving properties and introduces a necessary condition akin to Riesz frame characterizations.

Findings

Small perturbations can preserve woven pair properties under certain conditions.

The paper establishes a necessary condition for woven pairs resembling Riesz frame criteria.

Results extend and complete existing literature on woven frames.

Abstract

In this note, we prove some results related to small perturbations of a frame for a Hilbert space $\mathcal{H}$ in order to have a woven pair for $\mathcal{H}$. Our results complete those known in the literature. In addition we study a necessary condition for a woven pair, that resembles a characterization for Riesz frames.