Controlled K-operator frame for $End_\mathcal{A}^\ast (\mathcal{H})$

TL;DR

This paper introduces the concept of Controlled K-operator frames within the context of adjointable operators on Hilbert C*-modules, extending frame theory from Hilbert spaces to this broader setting.

Contribution

It defines and establishes foundational results for Controlled K-operator frames in Hilbert C*-modules, expanding the scope of frame theory.

Findings

Defined Controlled K-operator frames for $End_{\mathcal{A}}^{\ast}(\mathcal{H})$

Proved key properties and theorems related to these frames

Extended frame theory to the setting of Hilbert C*-modules

Abstract

Frame Theory has a great revolution for recent years. This theory has been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. In this paper, we introduce the concept of Controlled K-operator frame for the space $End_{\mathcal{A}}^{\ast}(\mathcal{H})$ of all adjointable operators on a Hilbert $\mathcal{A}$-module $\mathcal{H}$ and we establish some results.