Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space

2014 ◽  
Vol 220 (2) ◽  
pp. 141-156 ◽  
Author(s):  
Yong Chen ◽  
Young Joo Lee ◽  
Tao Yu
Keyword(s):  
Dirichlet Space ◽  
Multiplication Operators ◽  
Unitary Equivalence

scholarly journals Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces

2017 ◽  
Vol 4 (1) ◽  
pp. 84-119 ◽  
Author(s):  
Caixing Gu ◽  
Shuaibing Luo ◽  
Jie Xiao
Keyword(s):  
Bergman Space ◽  
Blaschke Product ◽  
Riemann Surfaces ◽  
Dirichlet Space ◽  
Multiplication Operator ◽  
Multiplication Operators ◽  
Finite Blaschke Product ◽  
Full Characterization ◽  
Reducing Subspaces

AbstractThis paper gives a full characterization of the reducing subspaces for the multiplication operator Mϕ on the Dirichlet space with symbol of finite Blaschke product ϕ of order 5I 6I 7. The reducing subspaces of Mϕ on the Dirichlet space and Bergman space are related. Our strategy is to use local inverses and Riemann surfaces to study the reducing subspaces of Mϕ on the Bergman space. By this means, we determine the reducing subspaces of Mϕ on the Dirichlet space and answer some questions of Douglas-Putinar-Wang in [6].

scholarly journals On unitary equivalence of invariant subspaces of the Dirichlet space

2010 ◽  
Vol 196 (2) ◽  
pp. 143-150 ◽  
Author(s):  
Kunyu Guo ◽  
Liankuo Zhao
Keyword(s):  
Dirichlet Space ◽  
Invariant Subspaces ◽  
Unitary Equivalence

Semigroups of Composition Operators on the Dirichlet Space

1996 ◽  
Vol 30 (1-2) ◽  
pp. 165-173 ◽  
Author(s):  
Aristomenis G. Siskakis
Keyword(s):  
Composition Operators ◽  
Dirichlet Space
Sign in / Sign up

Export Citation Format

Share Document