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Dunford-Pettis Multilinear Operators and their variations: A revisit to the classic concepts of Operator Ideals

Joilson Ribeiro, Fabricio Santos

Abstract

In this paper, we will address broader concepts for Dunford-Pettis operators, presenting new classes and results that correlate this class with others already well-studied in the literature, as well as an approach outside the origin. We also investigate the inclusion results and conditions for the coincidence of this class with others previously studied and also with new classes that will emerge throughout this text.

Dunford-Pettis Multilinear Operators and their variations: A revisit to the classic concepts of Operator Ideals

Abstract

In this paper, we will address broader concepts for Dunford-Pettis operators, presenting new classes and results that correlate this class with others already well-studied in the literature, as well as an approach outside the origin. We also investigate the inclusion results and conditions for the coincidence of this class with others previously studied and also with new classes that will emerge throughout this text.
Paper Structure (4 sections, 21 theorems, 105 equations)

This paper contains 4 sections, 21 theorems, 105 equations.

Table of Contents

  1. Introduction and background
  2. Dunford-Pettis Multilinear Operators and Homogeneous Polynomials Everywhere
  3. Weak Dunford-Pettis Multilinear Operators
  4. Weak* Dunford Pettis Multilinear Operators

Key Result

Proposition 2.4

Let $m \in \mathbb{N}$, $E_1,\dots, E_m$ and $F$ be Banach spaces. Then, $\mathcal{L_{DP}^{\text{ev}}}(E_1,\dots, E_m; F)$ is a closed subset of $\mathcal{L_{DP}}(E_1,\dots, E_m; F)$.

Theorems & Definitions (53)

  • Definition 2.1
  • Definition 2.2
  • Remark 2.3
  • Proposition 2.4
  • proof
  • Corollary 2.5
  • Proposition 2.6
  • proof
  • Theorem 2.7
  • proof
  • ...and 43 more