Abstract
Controlled frames have been the subject of interest because of its ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the concepts of controlled g−fusion frame and controlled K−g−fusion frame in Hilbert C∗−modules and we give some properties. Also, we study the perturbation problem of controlled K−g−fusion frame. Moreover, an illustrative example is presented to support the obtained results.
Highlights
Frames for Hilbert spaces were introduced by Duffin and Schaefer [4] in 1952 to study some deep problems in nonharmonic Fourier series by abstracting the fundamental notion of Gabor [6] for signal processing
Rashidi and Rahimi [10] are introduced the concept of Controlled frames in Hilbert C∗−modules
[11] Let {Wj }j∈J be a sequence of orthogonally complemented closed submodules of H and T ∈ EndA∗ (H) invertible, if T is invertible and (T ∗T) Wj ⊂ Wj for each j ∈ J, {T Wj }j∈J is a sequence of orthogonally complemented closed submodules and PWj T ∗ = PWj T ∗PT Wj
Summary
Frames for Hilbert spaces were introduced by Duffin and Schaefer [4] in 1952 to study some deep problems in nonharmonic Fourier series by abstracting the fundamental notion of Gabor [6] for signal processing. Many generalizations of the concept of frame have been defined in Hilbert C∗-modules [5, 7, 9, 13– 17]. Controlled frames in Hilbert spaces have been introduced by P. Rashidi and Rahimi [10] are introduced the concept of Controlled frames in Hilbert C∗−modules. Let GL+(H) be the set of all positive bounded linear invertible operators on H with bounded inverse. : H × H → A, such that is sesquilinear, positive definite and respects the module action.
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