Dual Fusion Frames

TL;DR

This paper introduces a new concept of dual fusion frames in infinite-dimensional Hilbert spaces, overcoming previous technical issues and demonstrating that these duals often behave like traditional dual frames, with examples of non-canonical duals.

Contribution

It extends the notion of dual fusion frames beyond the canonical case, resolving technical problems related to the synthesis operator in infinite dimensions.

Findings

Dual fusion frames can behave similarly to dual frames in many cases.

Examples of non-canonical dual fusion frames are provided.

The new definition overcomes previous technical difficulties.

Abstract

The definition of dual fusion frame presents technical problems related to the domain of the synthesis operator. The notion commonly used is the analogous to the canonical dual frame. Here a new concept of dual is studied in infinite-dimensional separable Hilbert spaces. It extends the commonly used notion and overcomes these technical difficulties. We show that with this definition in many cases dual fusion frames behave similar to dual frames. We exhibit examples of non-canonical dual fusion frames.