Generalized p-fusion frame in separable Banach space

TL;DR

This paper extends the concepts of g-fusion frames and gf-Riesz bases from Hilbert spaces to Banach spaces, exploring their properties, perturbations, and constructions in product spaces.

Contribution

It introduces the generalized p-fusion frame in Banach spaces, develops their properties, and constructs examples in product and tensor spaces, expanding the theoretical framework.

Findings

Properties of g-fusion frames in Banach spaces established

Perturbation results for g-fusion frames derived

Construction of g-p-fusion frames in product and tensor spaces

Abstract

Concepts of g-fusion frame and gf-Riesz basis in a Hilbert to a Banach space is being presented. Some properties of g-fusion frame and gf-Riesz basis in Banach space have been developed. We discuss perturbation results of g-fusion frame in a Banach space. Finally, we construct g-p-fusion frames in Cartesian product of Banach spaces and tensor product of Banach spaces.