Integral operator frames on Hilbert \(C^{*}\)-modules

Abstract

Introduced by Duffin and Schaefer as a part of their work on nonhamonic Fourier 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 \({\mathcal {H}}\) and we give some new properties 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.