Multiplication operators on Sobolev disk algebra  

作　　者：WANG Zongyao LIU Yiqiang 

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

出　　处：《Science China Mathematics》2005年第10期1395-1410,共16页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.10071020).

摘　　要：In this paper,we study the algebra consisting of analytic functions in the Sobolev space W^(2,2) (D) (D is the unit disk),called the Sobolev disk algebra,explore the properties of the multiplication operators M_f on it and give the characterization of the corn- mutant algebra A′(M_f) of M_f.We show that A′(M_f) is commutative if and only if M_f~* is a Cowen-Douglas operator of index 1.In this paper, we study the algebra consisting of analytic functions in the Sobolev space W2,2(D) (D is the unit disk), called the Sobolev disk algebra, explore the properties of the multiplication operators Mf on it and give the characterization of the commutant algebra A'(Mf) of Mf. We show that A'(Mf) is commutative if and only if Mf* is a Cowen-Douglas operator of index 1.

关 键 词：SOBOLEV DISK algebra  MULTIPLICATION operators  commutant. 

分 类 号：N[自然科学总论]