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K-biframes in Hilbert spaces

Abdelilah Karara, Mohamed Rossafi

Abstract

In this paper, we introduce a new concept of K-biframes for Hilbert spaces. We then examine several characterizations with the assistance of a biframe operator. Moreover, we investigate their properties from the perspective of operator theory by establishing various relationships and properties.

K-biframes in Hilbert spaces

Abstract

In this paper, we introduce a new concept of K-biframes for Hilbert spaces. We then examine several characterizations with the assistance of a biframe operator. Moreover, we investigate their properties from the perspective of operator theory by establishing various relationships and properties.
Paper Structure (4 sections, 16 theorems, 84 equations)

This paper contains 4 sections, 16 theorems, 84 equations.

Table of Contents

  1. Introduction
  2. Notation and preliminaries
  3. $K$-biframes in Hilbert spaces
  4. Operators on $K$-biframes for $\mathcal{H}$

Key Result

Theorem 2.3

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
  • Definition 2.2
  • Theorem 2.3
  • Definition 2.4
  • Theorem 2.5
  • Definition 2.6
  • Definition 3.1
  • Remark 3.2
  • Example 3.3
  • Definition 3.4
  • ...and 31 more