文献类型：期刊文献

英文题名：Geometric constructions of thin Blaschke products and reducing subspace problem

作者：Guo, Kunyu[1];Huang, Hansong[2]

机构：[1]Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China;[2]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2014

卷号：109

起止页码：1050

外文期刊名：PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000344232800007)】；

基金：This work is partially supported by NSFC (11001078; 11371096) and 'Chen Guang' project (11CG10).

语种：英文

摘要：In this paper, we mainly study geometric constructions of thin Blaschke products and reducing subspace problem of multiplication operators induced by such symbols on the Bergman space. Considering such multiplication operators, we present a representation of those operators commuting with both and . It is shown that for 'most' thin Blaschke products , is irreducible, that is, has no nontrivial reducing subspace; and such a thin Blaschke product is constructed. As an application of the methods, it is proved that for 'most' finite Blaschke productshas exactly two minimal reducing subspaces. Furthermore, under a mild condition, we get a geometric characterization for when defined by a thin Blaschke product has a nontrivial reducing subspace.