文献类型：期刊文献

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

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

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2009

卷号：52

期号：1

起止页码：142

外文期刊名：SCIENCE IN CHINA SERIES A-MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000264272900012)】；

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

语种：英文

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

摘要：Let R(D) be the algebra generated in Sobolev space W-22(D) by the rational functions with poles outside the unit disk (D) over bar. In this paper the multiplication operators M-g on R(D) is studied and it is proved that M-g similar to M-zn 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.