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Continuous K-biframes in Hilbert spaces

Abdelilah Karara, Mohamed Rossafi

Abstract

In this paper, we will introduce the concept of a continuous K-biframe for Hilbert spaces and we present various examples of continuous K-biframes. Furthermore, we investigate their characteristics from the perspective of operator theory by establishing various properties.

Continuous K-biframes in Hilbert spaces

Abstract

In this paper, we will introduce the concept of a continuous K-biframe for Hilbert spaces and we present various examples of continuous K-biframes. Furthermore, we investigate their characteristics from the perspective of operator theory by establishing various properties.
Paper Structure (3 sections, 10 theorems, 61 equations)

This paper contains 3 sections, 10 theorems, 61 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Continuous $K$-biframe in Hilbert spaces

Key Result

Theorem 2.3

Douglas Let $\mathcal{H}$ be a Hilbert space and $\mathcal{T}_{1},\mathcal{T}_{2}\in\mathcal{B}(\mathcal{H})$. The following statements are equivalent:

Theorems & Definitions (26)

  • Definition 2.1
  • Definition 2.2
  • Theorem 2.3
  • Definition 3.1
  • Remark 3.2
  • Example 3.3
  • Example 3.4
  • Definition 3.5
  • Proposition 3.6
  • proof
  • ...and 16 more