Some identities and inequalities for g-fusion frames

TL;DR

This paper introduces new identities, equalities, and inequalities for g-fusion frames in Hilbert spaces, extending recent theoretical developments and leveraging dual frames.

Contribution

It presents a novel identity for g-frames and derives new inequalities for g-fusion frames using dual frames, expanding the theoretical framework.

Findings

New identity for g-frames derived

New inequalities for g-fusion frames established

Extensions of existing theoretical results

Abstract

G-fusion frames which are obtained from the combination of g-frames and fusion frames were recently introduced for Hilbert spaces. In this paper, we present a new identity for g-frames which was given by Najati in a special case. Also, by using the idea of this identity and their dual frames, some equalities and inequalities will be presented for g-fusion frames.