# Perturbation of Continuous Frames on Quaternionic Hilbert Spaces

## TL;DR

This paper extends the theory of frame perturbations to quaternionic Hilbert spaces, analyzing the stability of continuous frames, Bessel, and Riesz families in a non-commutative setting.

## Contribution

It introduces the perturbation analysis of continuous frames and related families in quaternionic Hilbert spaces, expanding the scope beyond complex spaces.

## Key findings

- Established perturbation results for continuous frames in quaternionic spaces
- Analyzed stability of Bessel and Riesz families under perturbations
- Extended discrete frame perturbation theory to non-commutative quaternionic setting

## Abstract

In this note, following the theory of discrete frame perturbations in a complex Hilbert space, we examine perturbation of rank $n$ continuous frame, rank $n$ continuous Bessel family and rank $n$ continuous Riesz family in a non-commutative setting, namely in a right quaternionic Hilbert space.