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Distributional and mean Li--Yorke chaos for weighted shifts on Fréchet sequence spaces

João V. A. Pinto

Abstract

In this paper, we give characterizations of distributional chaos and mean Li$-$Yorke chaos for weighted backward shifts acting on general Fréchet sequence spaces. As an application, we derive criteria for these two types of chaos in the setting of Köthe sequence spaces $λ_p(A,J)$ for $p \in \{0\}\cup [1, \infty)$ and $J=\mathbb{N}$ or $J=\mathbb{Z}$.

Distributional and mean Li--Yorke chaos for weighted shifts on Fréchet sequence spaces

Abstract

In this paper, we give characterizations of distributional chaos and mean LiYorke chaos for weighted backward shifts acting on general Fréchet sequence spaces. As an application, we derive criteria for these two types of chaos in the setting of Köthe sequence spaces for and or .
Paper Structure (4 sections, 17 theorems, 78 equations)

This paper contains 4 sections, 17 theorems, 78 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Distributional chaos
  4. Mean Li--Yorke chaos

Key Result

Theorem 11

Nilson0 Let $T$ be a continuous linear operator on a Fréchet space $Y$. Then, the following statements are equivalent:

Theorems & Definitions (45)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Example 7
  • Example 8
  • Definition 9
  • Definition 10
  • ...and 35 more