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

POWERS OF COMPOSITION OPERATORS: ASYMPTOTIC BEHAVIOUR ON BERGMAN, DIRICHLET AND BLOCH SPACES

2019 ◽  
Vol 108 (3) ◽  
pp. 289-320 ◽  
Author(s):  
W. ARENDT ◽  
I. CHALENDAR ◽  
M. KUMAR ◽  
S. SRIVASTAVA
Keyword(s):  
Asymptotic Behaviour ◽  
Banach Spaces ◽  
Composition Operators ◽  
Bloch Space ◽  
Bergman Spaces ◽  
Dirichlet Space ◽  
Complete Characterization ◽  
Weighted Bergman Spaces ◽  
Bloch Type Space ◽  
Spaces Of Holomorphic Functions

We study the asymptotic behaviour of the powers of a composition operator on various Banach spaces of holomorphic functions on the disc, namely, standard weighted Bergman spaces (finite and infinite order), Bloch space, little Bloch space, Bloch-type space and Dirichlet space. Moreover, we give a complete characterization of those composition operators that are similar to an isometry on these various Banach spaces. We conclude by studying the asymptotic behaviour of semigroups of composition operators on these various Banach spaces.

Composition operators on a local Dirichlet space

2002 ◽  
Vol 87 (1) ◽  
pp. 433-450 ◽  
Author(s):  
Donald Sarason ◽  
Jorge-Nuno O. Silva
Keyword(s):  
Composition Operators ◽  
Dirichlet Space

scholarly journals On the closed range problem for composition operators on the Dirichlet space

2019 ◽  
Vol 6 (1) ◽  
pp. 76-81
Author(s):  
Nina Zorboska
Keyword(s):  
Toeplitz Operators ◽  
Composition Operators ◽  
Dirichlet Space ◽  
Closed Range ◽  
Berezin Transforms

Abstract We characterize closed range composition operators on the Dirichlet space for a particular class of composition symbols. The characterization relies on a result about Fredholm Toeplitz operators with BMO1 symbols, and with Berezin transforms of vanishing oscillation.

scholarly journals Approximation numbers of composition operators on the Dirichlet space

2015 ◽  
Vol 53 (1) ◽  
pp. 155-175 ◽  
Author(s):  
Pascal Lefèvre ◽  
Daniel Li ◽  
Hervé Queffélec ◽  
Luis Rodríguez-Piazza
Keyword(s):  
Composition Operators ◽  
Dirichlet Space ◽  
Approximation Numbers
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