Some Generalizations of Frames in Hilbert Modules

Mohamed Rossafi,Samir Kabbaj,Seppo Hassi

doi:10.1155/2021/5522671

Abstract

Frames play significant role in various areas of science and engineering. In this paper, we introduce the concept of frames for the set of all adjointable operators from ℋ to K and their generalizations. Moreover, we obtain some new results for generalized frames in Hilbert modules.

Highlights

Introduction and Preliminaries e concept of frames in Hilbert spaces has been introduced by Duffin and Schaeffer [1] in 1952 to study some deep problems in nonharmonic Fourier series
Frames have been used in signal processing, image processing, data compression, and sampling theory
We begin this section with the following hTeorem

Summary

Introduction

Introduction andPreliminaries e concept of frames in Hilbert spaces has been introduced by Duffin and Schaeffer [1] in 1952 to study some deep problems in nonharmonic Fourier series. We call a sequence 􏼈Λi ∈ End∗A(H, Vi): i ∈ I􏼉 a g-frame in Hilbert A-module H with respect to 􏼈Vi: i ∈ I􏼉 if there exist two positive constants C, D, such that, for all x ∈ H, C〈x, x〉A ≤ 􏽘 〈Λix, Λix〉A ≤ D〈x, x〉A, (5)

Results

Conclusion