Controlled $K$-Fusion Frame for Hilbert Spaces

TL;DR

This paper introduces controlled $K$-fusion frames in Hilbert spaces, extending existing fusion frame concepts, and investigates their properties, characterizations, and stability under perturbations.

Contribution

It generalizes controlled fusion frames to controlled $K$-fusion frames and explores their fundamental properties and stability conditions.

Findings

Generalized controlled $K$-fusion frames for Hilbert spaces

Characterizations of controlled Bessel $K$-fusion sequences

Stability conditions under perturbation

Abstract

$K$-fusion frames are a generalization of fusion frames in frame theory. In this paper, we extend the concept of controlled fusion frames to controlled $K$-fusion frames, and we develop some results on the controlled $K$-fusion frames for Hilbert spaces, which generalized some well known of controlled fusion frames case. also we discuss some characterizations of controlled Bessel $K$-fusion sequences and of controlled Bessel $K$-fusion. Further, we analyse stability conditions of controlled $K$-fusion frames under perturbation.