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Construction of continuous K-g-Frames in Hilbert $C^{\ast}$-Modules

Abdelilah Karara, Mohamed Rossafi, Mohammed Klilou, Samir Kabbaj

Abstract

In this work, we provide some constructions and the sum of new continuous K-g-frames in Hilbert$C^{\ast}$-Modules. We provide certain necessary and sufficient conditions for some adjointable operators on $\mathcal{H}$, under which new continuous K-g-frames can be retrieved from those that already exist. Additionally, we discuss the sum of continuous K-g-frames, discover some of their characterizations, and offer some adjointable operators to construct new continuous K-g-frames from the previous ones.

Construction of continuous K-g-Frames in Hilbert $C^{\ast}$-Modules

Abstract

In this work, we provide some constructions and the sum of new continuous K-g-frames in Hilbert-Modules. We provide certain necessary and sufficient conditions for some adjointable operators on , under which new continuous K-g-frames can be retrieved from those that already exist. Additionally, we discuss the sum of continuous K-g-frames, discover some of their characterizations, and offer some adjointable operators to construct new continuous K-g-frames from the previous ones.
Paper Structure (3 sections, 14 theorems, 65 equations)

This paper contains 3 sections, 14 theorems, 65 equations.

Table of Contents

  1. Introduction and preliminaries
  2. Some new constructing of c-K-g-frames in Hilbert $C^{\ast}$-modules
  3. Sum of c-K-g-frames in Hilbert $C^*$ modules

Key Result

Lemma 1.4

Pas. Let $\mathcal{H}$ be Hilbert $\mathcal{A}$-module. If $\mathcal{T}\in End_{\mathcal{A}}^{\ast}(\mathcal{H})$, then

Theorems & Definitions (29)

  • Definition 1.1
  • Definition 1.2
  • Definition 1.3
  • Lemma 1.4
  • Lemma 1.5
  • Definition 1.6
  • Lemma 1.7
  • Lemma 1.8
  • Theorem 1.9
  • Definition 1.10
  • ...and 19 more