K-g-fusion frames in Hilbert C∗-modules

Abstract

In this paper, we introduce the concepts of g-fusion frame and K-g-fusion frame in Hilbert C∗-modules and we give some properties. Also, we study the stability problem of g-fusion frame. The presented results extend, generalize and improve many existing results in the literature.

Controlled K−g−Fusion Frames in Hilbert C∗−Modules

“…(2) There exists µ > 0 such that (T ) * z ≤ µ T * z for all z ∈ L. Lemma 2.7. [11] Let {W j } j∈J be a sequence of orthogonally complemented closed submodules of H and T ∈ End * A (H) invertible, if T * T W j ⊂ W j for each j ∈ J, then {T W j } j∈J is a sequence of orthogonally complemented closed submodules and P W j T * = P W j T * P T W j .…”

“…Definition 3.1. [11] Let {W j } j∈J be a sequence of closed submodules orthogonally complemented of H, {v j } j∈J be a family of weights in A, ie., each v j is positive invertible element frome the center of A and Λ j ∈ End * A (H, H j ) for each j ∈ J. We say that Λ = {W j , Λ j , v j } j∈J is a g−fusion frame for H if there exists 0…”

Some Properties of Controlled K-g-Frames in Hilbert C∗-Modules

“…Many generalizations of the concept of frame have been defined in Hilbert C * -modules [3,5,6,9,[11][12][13][14][15]. Controlled frames in Hilbert spaces have been introduced by P. Balazs [1] to improve the numerical efficiency of iterative algorithms for inverting the frame operator.…”

Woven generalized fusion frame in Hilbert $C^{\ast}-$module

“…In 2016, Z. Xiang and Y. Li [23] give a generalization of g−frames for operators in Hilbert C * -modules. Recently, Fakhr-dine Nhari et al [15] introduced the concepts of g-fusion frame and K-g-fusion frame in Hilbert C * -modules. Bemrose et al [4] introduced a new concept of weaving frames in separable Hilbert spaces.…”

“…5 [15]. Let {W i } i∈I be a sequence of closed orthogonally complemented submodules of H, {v i } i∈I be a familly of positive weights in A, i.e., each v i is a positive invertible element from the center of the C * −algebra A and Λ i ∈ End * A (H, H i ) for all i ∈ I.…”