On the duality of c-fusion frames in Hilbert spaces

TL;DR

This paper explores the duality concept for continuous fusion frames in Hilbert spaces, introduces the new notion of Q-dual to address existing limitations, and investigates its properties.

Contribution

It extends the duality theory for fusion frames by defining and analyzing Q-duals for continuous fusion frames in Hilbert spaces.

Findings

Duals of c-fusion frames may not always exist

Q-duals provide a new framework for duality in c-fusion frames

Properties of Q-duals are systematically studied

Abstract

Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may not be defined. To overcome this problem, the new concept namely Q-dual for c-fusion frames will be defined and some of its properties will be investigated.