# On weaving frames in Hilbert spaces

## TL;DR

This paper investigates the properties and conditions for weaving frames in Hilbert spaces, providing new characterizations, stability results, and conditions involving synthesis operators to advance understanding of frame weaving.

## Contribution

It introduces novel properties and operator-based characterizations of weaving frames, along with stability results under perturbations and invertible transformations.

## Key findings

- New properties of weaving frames are established.
- Conditions involving synthesis operators are identified.
- Woven frames are shown to be stable under invertible operators and small perturbations.

## Abstract

In this paper, we obtain some new properties of weaving frames and present some conditions under which a family of frames is woven in Hilbert spaces. Some characterizations of weaving frames in terms of operators are given. We also give a condition associated with synthesis operators of frames such that the sequence of frames is woven. Finally, for a family of woven frames, we show that they are stable under invertible operators and small perturbations.