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 bounded right \(\mathbb {H}\)-linear operator and \(\{u_i\}_{i \in I}\) is a frame. We also show that every bounded, positive, invertible right \(\mathbb {H}\)-linear operator arises as a frame operator.