Generalized fusion frame in Quaternionic Hilbert spaces

TL;DR

This paper introduces and characterizes generalized fusion frames in quaternionic Hilbert spaces, providing a framework for their construction using invertible bounded operators.

Contribution

It extends the concept of fusion frames to quaternionic Hilbert spaces and offers a method to construct g-fusion frames via invertible operators.

Findings

Characterization of generalized fusion frames using frame operators

Construction of g-fusion frames with invertible bounded operators

Extension of fusion frame theory to quaternionic Hilbert spaces

Abstract

We introduce the notion of a generalized fusion frame in quaternionic Hilbert space. A characterization of generalized fusion frame in quaternionic Hilbert space with the help of frame operator is being discussed. Finally, we construct g-fusion frame in quaternionic Hilbert space using invertible bounded right Q-linear operator on quaternionic Hilbert space.