Integral Operator Frames on Hilbert C*-modules

TL;DR

This paper introduces the concept of integral operator frames for adjointable operators on Hilbert C*-modules, expanding the theoretical framework and providing new properties and examples to demonstrate their applicability.

Contribution

It presents a novel concept of integral operator frames in the context of Hilbert C*-modules, along with new properties, results, and illustrative examples.

Findings

Established new properties of integral operator frames.

Provided examples demonstrating the construction and utility of these frames.

Extended the theory of frames to the setting of Hilbert C*-modules.

Abstract

Introduced by Duffin and Schaefer as a part of their work on nonhamonic fourrier series in 1952, the theory of frames has undergone a very interesting evolution in recent decades following the multiplicity of work carried out in this field. In this work, we introduce a new concept that of integral operator frame for the set of all adjointable operators on a Hilbert C*-modules H and we give some new propertis relating for some construction of integral operator frame, also we establish some new results. Some illustrative examples are provided to advocate the usability of our results.