Dual and multiplier of $K$-fusion frames

TL;DR

This paper introduces $K$-fusion frames, explores their duality, and establishes multipliers for reconstructing elements in the range of a bounded linear operator $K$, advancing frame theory.

Contribution

It presents the concept of $K$-fusion frames, their duality, and $K$-fusion frame multipliers, providing new tools for reconstruction in frame theory.

Findings

Defined $K$-fusion frames and their duals

Studied the relation between local frames and their duals

Established $K$-fusion frame multipliers for reconstruction

Abstract

In this paper, we introduce the concept of $K$-fusion frames and propose the duality for such frames. The relation between the local frames of $K$-fusion frames with their dual is studied. The elements from the range of a bounded linear operator $K$ can be reconstructed by $K$-frames. Also, we establish $K$-fusion frame multipliers and investigate reconstruction of the range of $K$ by them.