文献类型：期刊文献

英文题名：ON MULTIPLICATION OPERATORS ON THE BERGMAN SPACE: SIMILARITY, UNITARY EQUIVALENCE AND REDUCING SUBSPACES

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：2011

卷号：65

期号：2

起止页码：355

外文期刊名：JOURNAL OF OPERATOR THEORY

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000290824300007)】；

基金：This work is partially supported by Laboratory of Mathematics for Nonlinear Science, Fudan University, NSFC(11001078) and NSFC(10525106) and NKBRPC (2006CB805905).

语种：英文

外文关键词：Bergman space; finite Blaschke product; minimal reducing subspaces; unitary equivalence; similarity

摘要：In this paper, we study similarity, unitary equivalence and reducing subspace problems of multiplication operators with symbols of finite Blaschke products on the Bergman space L-a(2)(D). By using Rudin's method, we establish a representation theorem of L-a(2)-functions related to a given finite Blaschke product. As an immediate consequence, one sees that for two finite Blaschke products B-1, B-2, M-B1 is similar to M-B2 if and only if deg B-1 = deg B-2. By a different method, this similarity result also was independently obtained by Jiang and Li. Then we turn to the study of reducing subspaces of multiplication operators. It is shown that if B is a finite Blaschke product with deg B <= 6, then the number of minimal reducing subspaces of M-B is at most deg B. The best previous known results were for the cases of deg B = 2, 3, 4.