Controlled continuous $g$-frames and their duals in Hilbert spaces

TL;DR

This paper extends the theory of continuous g-frames in Hilbert spaces by introducing controlled continuous g-frames and their duals, providing new characterizations and properties for these mathematical structures.

Contribution

It introduces the concept of controlled continuous dual g-frames and characterizes all such duals for a given controlled continuous g-frame.

Findings

Defined controlled continuous g-frames in Hilbert spaces

Characterized controlled continuous dual g-frames

Established properties and duality relations for these frames

Abstract

In this paper, we characterize and study the concept of controlled continuous $g$-frame which is an extension of continuous $g$-frame in Hilbert spaces. We introduce the concept of controlled continuous dual $g$-frame and observe some interesting properties of it. Finally, we characterize all controlled continuous dual $g$-frames of a controlled continuous $g$-frame.