Frames and Operators on 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 $\{L{u}_i{\}}_{i\in I}$, where $L$ is a right $\mathbb{H}$-linear bounded operator and $\{u_i{\}}_{i\in I}$ is a frame.