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Demi Weakly Dunford-Pettis on Banach Spaces

Joilson Ribeiro, Fabricio Santos

Abstract

In this paper, our main goal is to define the class of weakly Demi Dunford-Pettis applications. We also study their relationship with the classes of weakly Dunford-Pettis and Demi Dunford-Pettis operators, including a condition where these operators coincide with Demi Dunford-Pettis and Demicompacts. In the last section, we study some of the behavior of this class in the Banach Lattice environment.

Demi Weakly Dunford-Pettis on Banach Spaces

Abstract

In this paper, our main goal is to define the class of weakly Demi Dunford-Pettis applications. We also study their relationship with the classes of weakly Dunford-Pettis and Demi Dunford-Pettis operators, including a condition where these operators coincide with Demi Dunford-Pettis and Demicompacts. In the last section, we study some of the behavior of this class in the Banach Lattice environment.
Paper Structure (3 sections, 15 theorems, 66 equations)

This paper contains 3 sections, 15 theorems, 66 equations.

Table of Contents

  1. Introduction and background
  2. Demi Weakly Dunford-Pettis Operators
  3. Demi Weakly Dunford-Pettis Operators on Banach Lattices

Key Result

Proposition 2.2

Let $X$ be a Banach space. An operator $T\colon X \longrightarrow X$ is weakly demi Dunford–Pettis if, and oly if, for all $(x_j)_{j=1}^{\infty}$ in $X$ and $(f_j)_{j=1}^{\infty}$ in $X'$ with $x_j \overset{w}{\rightarrow} x$, $f_j \overset{w}{\rightarrow} f$ and $(x_j - T(x_j)) \overset{\|\cdot\|}{

Theorems & Definitions (36)

  • Definition 2.1
  • Proposition 2.2
  • proof
  • Proposition 2.3
  • proof
  • Example 2.4
  • Theorem 2.5
  • proof
  • Remark 2.6
  • Lemma 2.7
  • ...and 26 more