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K-bi-g-frames in Hilbert spaces

Abdelilah Karara, Mohamed Rossafi

Abstract

In this paper, we will introduce the new concept of K-bi-g-frames for Hilbert spaces. Then, we examine some characterizations with the help of a biframe operator. Finally, we investigate several results about the stability of K-bi-g-frames are produced via the use of frame theory methods.

K-bi-g-frames in Hilbert spaces

Abstract

In this paper, we will introduce the new concept of K-bi-g-frames for Hilbert spaces. Then, we examine some characterizations with the help of a biframe operator. Finally, we investigate several results about the stability of K-bi-g-frames are produced via the use of frame theory methods.
Paper Structure (5 sections, 18 theorems, 90 equations)

This paper contains 5 sections, 18 theorems, 90 equations.

Table of Contents

  1. Introduction
  2. Notation and preliminaries
  3. $K$-bi-$g$-frames in Hilbert spaces
  4. Operators on $K$-bi-$g$-frames in Hilbert Spaces
  5. Stability of $K$-bi-$g$-frames for Hilbert spaces

Key Result

Theorem 2.2

Abramovich$\mathcal{T} \in\mathcal{B}(\mathcal{H})$ is an injective and closed range operator if and only if there exists a constant $c>0$ such that $c\|x\|^2 \leq\|\mathcal{T} x\|^2$, for all $x \in \mathcal{H}$

Theorems & Definitions (41)

  • Definition 2.1
  • Theorem 2.2
  • Definition 2.3
  • Theorem 2.4
  • Lemma 2.5
  • Definition 3.1
  • Definition 3.2
  • Remark 3.3
  • Example 3.4
  • Definition 3.5
  • ...and 31 more