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Weighted Composition Operator on Fock Space

Rui Hu

Abstract

In this thesis, we establish a necessary and sufficient condition for a weighted composition operator to commute with a self-adjoint weighted composition operator on the Fock space, then obtain a sufficient condition for these commuting weighted composition operators to be normal.

Weighted Composition Operator on Fock Space

Abstract

In this thesis, we establish a necessary and sufficient condition for a weighted composition operator to commute with a self-adjoint weighted composition operator on the Fock space, then obtain a sufficient condition for these commuting weighted composition operators to be normal.
Paper Structure (3 sections, 12 theorems, 73 equations)

This paper contains 3 sections, 12 theorems, 73 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main Results

Key Result

Lemma 2.1

If $h\in F^2$, then for weighted composition operator $W_{f,\varphi}$ and $W_{g, \psi}$,we have Here and hereafter, we use $M_h$ to denote the multiplication operator with $h$ as the sign.

Theorems & Definitions (24)

  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Theorem 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • ...and 14 more