Toeplitz Operators on Dirichlet Spaces

2001 ◽  
Vol 17 (4) ◽  
pp. 643-648
Author(s):  
Yu Feng Lu ◽  
Shun Hua Sun
Keyword(s):  
Toeplitz Operators ◽  
Dirichlet Spaces

Toeplitz operators on Dirichlet spaces

1992 ◽  
Vol 15 (2) ◽  
pp. 325-342 ◽  
Author(s):  
Richard Rochberg ◽  
Zhijian Wu
Keyword(s):  
Toeplitz Operators ◽  
Dirichlet Spaces

scholarly journals Hyponormal Toeplitz Operators on the Dirichlet Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Puyu Cui ◽  
Yufeng Lu
Keyword(s):  
Toeplitz Operators ◽  
Dirichlet Space ◽  
Dirichlet Spaces ◽  
Harmonic Dirichlet Space

We completely characterize the hyponormality of bounded Toeplitz operators with Sobolev symbols on the Dirichlet space and the harmonic Dirichlet space.

scholarly journals Range Spaces of Co-Analytic Toeplitz Operators

2018 ◽  
Vol 70 (6) ◽  
pp. 1261-1283 ◽  
Author(s):  
Emmanuel Fricain ◽  
Andreas Hartmann ◽  
William T. Ross
Keyword(s):  
Toeplitz Operator ◽  
Toeplitz Operators ◽  
Boundary Behavior ◽  
Model Space ◽  
Orthogonal Complement ◽  
Dirichlet Spaces ◽  
Backward Shift ◽  
Weighted Dirichlet Spaces ◽  
General Abstract ◽  
Analytic Toeplitz Operator

AbstractIn this paper we discuss the range of a co-analytic Toeplitz operator. These range spaces are closely related to de Branges–Rovnyak spaces (in some cases they are equal as sets). In order to understand its structure, we explore when the range space decomposes into the range of an associated analytic Toeplitz operator and an identifiable orthogonal complement. For certain cases, we compute this orthogonal complement in terms of the kernel of a certain Toeplitz operator on the Hardy space, where we focus on when this kernel is a model space (backward shift invariant subspace). In the spirit of Ahern–Clark, we also discuss the non-tangential boundary behavior in these range spaces. These results give us further insight into the description of the range of a co-analytic Toeplitz operator as well as its orthogonal decomposition. Our Ahern–Clark type results, which are stated in a general abstract setting, will also have applications to related sub-Hardy Hilbert spaces of analytic functions such as the de Branges–Rovnyak spaces and the harmonically weighted Dirichlet spaces.

Toeplitz Operators on Dirichlet Spaces

2001 ◽  
Vol 17 (4) ◽  
pp. 643-648 ◽  
Author(s):  
Yu Feng Lu ◽  
Shun Hua Sun
Keyword(s):  
Toeplitz Operators ◽  
Dirichlet Spaces

scholarly journals Toeplitz Operators on Arveson and Dirichlet Spaces

2007 ◽  
Vol 58 (1) ◽  
pp. 1-33 ◽  
Author(s):  
Daniel Alpay ◽  
H. Turgay Kaptanoğlu
Keyword(s):  
Toeplitz Operators ◽  
Dirichlet Spaces
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