文献类型：期刊文献

中文题名：Finite Blaschke product and the multiplication operators on Sobolev disk algebra

英文题名：Finite Blaschke product and the multiplication operators on Sobolev disk algebra

作者：ZongYao Wang (1)[1];RuiFang Zhao (1)[1];YongFei Jin (1)[1];

机构：[1]1. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China;

年份：2009

卷号：52

期号：1

起止页码：142

中文期刊名：中国科学：数学英文版

外文期刊名：SCIENCE CHINA Mathematics

收录：Scopus

基金：supported by the National Natural Science Foundation of China (Grant No. 10471041)

语种：英文

中文关键词：finite;Blaschke;product;multiplication;operators;Sobolev;disk;algebra;similarity

外文关键词：finite Blaschke product; multiplication operators; Sobolev disk algebra; similarity; 47B38; 47A15;

摘要：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 the multiplication operators Mg on R(D) is studied and it is proved that Mg ～ Mzn if and only if g is an n-Blaschke product. Furthermore, if g is an n-Blaschke product, then Mg has uncountably many Banach reducing subspaces if and only if n > 1.
Let R(D) be the algebra generated in Sobolev space W 22(D) by the rational functions with poles outside the unit disk $ \overline D $ . In this paper the multiplication operators M g on R(D) is studied and it is proved that M g ～ $ M_{z^n } $ if and only if g is an n-Blaschke product. Furthermore, if g is an n-Blaschke product, then M g has uncountably many Banach reducing subspaces if and only if n > 1.