International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 378217, 17 pages
http://dx.doi.org/10.1155/2012/378217
Research Article

A Similarity Invariant and the Commutant of some Multiplication Operators on the Sobolev Disk Algebra

Ruifang Zhao

Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China

Received 31 March 2012; Accepted 19 July 2012

Academic Editor: Gideon Schechtman

Copyright © 2012 Ruifang Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let R(𝔻) be the algebra generated in Sobolev space W22(𝔻) by the rational functions with poles outside the unit disk 𝔻¯. In this paper, we study the similarity invariant of the multiplication operators Mg in ℒ(R(𝔻)), when g is univalent analytic on 𝔻 or Mg is strongly irreducible. And the commutants of multiplication operators whose symbols are composite functions, univalent analytic functions, or entire functions are studied.