Title page for ETD etd-08142006-110124


Type of Document Dissertation
Author Liang, Xiaoming
URN etd-08142006-110124
Title A class of weighted Bergman spaces, reducing subspaces for multiple weighted shifts, and dilatable operators
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
No Advisors Found
Keywords
  • Weighted Shift
  • Reducing Subspace
  • Invariant Subspace
  • Super-Dilatable Operator
Date of Defense 1996-08-15
Availability restricted
Abstract

This thesis consists of four chapters. Chapter 1 contains the preliminaries. We give the background, notation and some results needed for this work, and we describe our main results of this thesis.

In Chapter 2 we will introduce a class of weighted Bergman spaces. We then will discuss some properties about the multiplication operator, Mz , on them. We also characterize the dual spaces of these weighted Bergman spaces.

In Chapter 3 we will characterize the reducing subspaces of multiple weighted shifts. The reducing subspaces of the Bergman and the Dirichlet shift of multiplicity N are portrayed from this characterization.

In Chapter 4 we will introduce the class of super-isometrically dilatable operators and describe their elementary properties. We then will discuss an equivalent description of the invariant subspace lattice for the Bergman shift. We will also discuss the interpolating sequences on the bidisk. Finally, we will examine a special class of super-isometrically dilatable operators. One corollary of this work is that we will prove that the conlpression of the Bergman shift on two compliments of two invariant subspaces are unitarily equivalent if and only if the two invariant subspaces are equal.

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