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 ${Lu_i}{i \in I}$, where $L$ is a right $\mathbb{H}$-linear bounded operator and ${u_i}{i \in I}$ is a frame.