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Some classes of composition operators on Orlicz spaces

Z. Huang, Y. Estaremi

Abstract

The notions of expansivity and positive expansivity for composition operators on Orlicz spaces are investigated. In particular, necessary and sufficient conditions are given for a composition operator to be expansive, positively expansive, and uniformly expansive. Additionally, equivalent conditions for these concepts are provided in the case that the system is dissipative.

Some classes of composition operators on Orlicz spaces

Abstract

The notions of expansivity and positive expansivity for composition operators on Orlicz spaces are investigated. In particular, necessary and sufficient conditions are given for a composition operator to be expansive, positively expansive, and uniformly expansive. Additionally, equivalent conditions for these concepts are provided in the case that the system is dissipative.
Paper Structure (2 sections, 9 theorems, 92 equations)

This paper contains 2 sections, 9 theorems, 92 equations.

Table of Contents

  1. Introduction and Preliminaries
  2. Expansivity for composition operators

Key Result

Theorem 1.1

raor Let $\{f_n\}_{n\geq1}$ be a sequence in $L^{\Phi}(\mu)$ and $f\in L^{\Phi}(\mu)$. Then the following assertions hold: (a) If $\|f_n-f\|_{\Phi}\rightarrow 0$ (or equivalently $N_{\Phi}(f_n-f)\rightarrow 0$), then $\rho_{\Phi}(f_n)\rightarrow \rho_{\Phi}(f)$. The converse holds if $\Phi$ is $\tri

Theorems & Definitions (18)

  • Theorem 1.1
  • Proposition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Proposition 2.6
  • Theorem 2.7
  • proof
  • Theorem 2.8
  • ...and 8 more