On *-fusion frames for Hilbert C*-modules

TL;DR

This paper extends the concept of fusion frames to Hilbert C*-modules by introducing *-fusion frames, along with fundamental theoretical results, broadening the framework for analyzing structured submodules in operator algebra contexts.

Contribution

The paper introduces *-fusion frames for Hilbert C*-modules, generalizing fusion frames and establishing foundational properties in this new setting.

Findings

Defined *-fusion frames for Hilbert C*-modules

Proved fundamental properties of *-fusion frames

Extended fusion frame theory to operator algebra contexts

Abstract

Our main goal in this paper, is to generalize to Hilbert C*-modules the concept of fusion frames. Indeed we introduce the notion of *\~nfusion frames associated to weighted sequences of orthogonally complemented submodules of a Hilbert C*-module, and prove for such a *-fusion frames some fundamental results.