Generalized frames and controlled operators in Hilbert space

TL;DR

This paper extends the theory of controlled g-frames in Hilbert spaces by introducing new properties, constructions, and stability results, broadening the understanding of generalized frame systems.

Contribution

It generalizes existing results on controlled frames to controlled g-frames, providing new properties, constructions, and stability analysis.

Findings

New properties of controlled g-frames

Construction of new controlled g-frames from components

Stability results under small perturbations

Abstract

Controlled frames and g-frames were considered recently as generalizations of frames in Hilbert spaces. In this paper we generalize some of the known results in frame theory to controlled g-frames. We obtain some new properties of controlled g-frames and obtain new controlled g-frames by considering controlled g-frames for its components. And we obtain some new resolutions of the identity. Furthermore, we study the stabilities of controlled g-frames under small perturbations.