Characterizations of dual of K-frames in quaternionic Hilbert spaces

TL;DR

This paper explores the properties and characterizations of duals and approximate duals of K-frames in quaternionic Hilbert spaces, extending existing theory to cases with non-closed ranges.

Contribution

It provides new characterizations of K-duals and introduces the concept of approximate K-duals in quaternionic Hilbert spaces, especially when the range of K is not closed.

Findings

Characterization of K-duals via canonical K-duals

Introduction of approximate K-duals and their properties

Existence results for approximate K-duals

Abstract

Dual of K-frames in a right quaternionic Hilbert space has been recently introduced and studied by Ellouz[1]. In this paper, we study duals of K-frames and prove a characterization of a K-dual in terms of the canonical K-dual of a K-frame in the case when the range of K is not necessarily closed. Moreover, we defined and studied the Approximate K- Dual of a K-frame in a right quaternionic Hilbert space and proved various results for their existence.