Generalized fusion frame in tensor product of Hilbert spaces

TL;DR

This paper explores the properties of generalized fusion frames in tensor product Hilbert spaces, introduces the canonical dual, and discusses the frame operator for g-fusion Bessel sequences, advancing the theoretical framework of frame theory.

Contribution

It extends the concept of generalized fusion frames to tensor product Hilbert spaces and analyzes their duals and frame operators, providing new theoretical insights.

Findings

Properties of g-fusion frames in tensor product spaces described

Canonical dual g-fusion frames in tensor product spaces considered

Frame operator for g-fusion Bessel sequences presented

Abstract

Generalized fusion frame and some of their properties in tensor product of Hilbert spaces are described. Also, the canonical dual g-fusion frame in tensor product of Hilbert spaces is considered. Finally, the frame operator for a pair of g-fusion Bessel sequences in tensor product of Hilbert spaces is presented.