Frames and Operators on Quaternionic Hilbert spaces

TL;DR

This paper explores the theory of frames in quaternionic Hilbert spaces, characterizing them via operators and analyzing frames generated by bounded operators applied to existing frames.

Contribution

It provides a new characterization of frames in quaternionic Hilbert spaces and studies frames formed through bounded operators.

Findings

Characterization of frames via associated operators.

Analysis of frames generated by bounded operators.

Extension of frame theory to quaternionic Hilbert spaces.

Abstract

The aim of this work is to study frame theory in quaternionic Hilbert spaces. We provide a characterization of frames in these spaces through the associated operators. Additionally, we examine frames of the form $\{Lu_i\}_{i \in I}$, where $L$ is a right $\mathbb{H}$-linear bounded operator and $\{u_i\}_{i \in I}$ is a frame.