Controlled continuous $\ast$-$g$-Frames in Hilbert $C^{\ast}$-Modules

TL;DR

This paper introduces and studies controlled continuous $ extit{g}$-frames in Hilbert $C^{ ext{*}}$-modules, generalizing discrete frames and exploring their properties for advanced mathematical applications.

Contribution

It extends the concept of controlled $ extit{g}$-frames to continuous settings in Hilbert $C^{ ext{*}}$-modules, providing new theoretical insights.

Findings

Defined controlled continuous $ extit{g}$-frames in Hilbert $C^{ ext{*}}$-modules

Established properties and characterizations of these frames

Generalized discrete controlled $ extit{g}$-frames to continuous cases

Abstract

The frame theory is dynamic and exciting with various pure and applied mathematics applications. In this paper, we introduce and study the concept of Controlled Continuous $\ast$-$g$-Frames in Hilbert $C^{\ast}$-Modules, which is a generalization of discrete controlled $\ast$-$g$-Frames in Hilbert $C^{\ast}$-Modules. Also, we give some properties.