Abstract In this paper, we give a similarity classification for the multiplication operator Mg on the Sobolev disk algebra R（D） with g analytic on the closure of the unit disk D.
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 i...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.展开更多
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 prove...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.展开更多
In this paper, we study the invariant subspaces of the operator Mz on the Sobolev disk algebra R（D） and characterize the invariant subspace with finite codimension.
We prove the reducibility of analytic multipliers M_(φ)with a class of finite Blaschke products symbolφon the Sobolev disk algebra R(D).We also describe their nontrivial minimal reducing subspaces.
基金Supported by National Natural Science Foundation of China(Grant No.10901046)Foundation for the Author of National Excellent Doctoral Dissertation of China(Grant No.201116)
文摘Abstract In this paper, we give a similarity classification for the multiplication operator Mg on the Sobolev disk algebra R（D） with g analytic on the closure of the unit disk D.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10071020).
文摘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.
基金supported by the National Natural Science Foundation of China (Grant No. 10471041)
文摘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.
基金the National Natural Science Foundation of China (10471041)
文摘In this paper, we study the invariant subspaces of the operator Mz on the Sobolev disk algebra R（D） and characterize the invariant subspace with finite codimension.
文摘We prove the reducibility of analytic multipliers M_(φ)with a class of finite Blaschke products symbolφon the Sobolev disk algebra R(D).We also describe their nontrivial minimal reducing subspaces.
