Controlled $\ast$-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 beyond traditional Hilbert spaces.

Contribution

It defines and explores the properties of Controlled *-K-operator frames in Hilbert C*-modules, a novel extension of existing frame concepts.

Findings

Established foundational results for Controlled *-K-operator frames.

Extended frame theory from Hilbert spaces to Hilbert C*-modules.

Provided new tools for operator analysis in C*-module settings.

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 $\ast$-$K$-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.