Integral $K$-Operator Frames for $End_{\mathcal{A}}^{\ast}(\mathcal{H})$

TL;DR

This paper introduces the concept of integral K-operator frames for adjointable operators on Hilbert C*-modules, exploring their properties, constructions, and operator-preserving characteristics.

Contribution

It defines and studies a new class of frames called integral K-operator frames within the context of Hilbert C*-modules, providing foundational properties and operator relations.

Findings

Established properties of integral K-operator frames.

Analyzed constructions and operator-preserving aspects.

Presented new theoretical results in frame theory for C*-modules.

Abstract

In this work, we introduce a new concept of integral $K$-operator frame for the set of all adjointable operators from Hilbert $C^{\ast}$-modules $\mathcal{H}$ to it self noted $End_{\mathcal{A}}^{\ast}(\mathcal{H}) $. We give some propertis relating some construction of integral $K$-operator frame and operators preserving integral $K$-operator frame and we establish some new results.