Linear fractional composition operators on the Dirichlet space in the unit ball

2009 ◽  
Vol 52 (8) ◽  
pp. 1661-1670 ◽  
Author(s):  
ZeHua Zhou ◽  
Cheng Yuan
Keyword(s):  
Unit Ball ◽  
Fractional Composition ◽  
Composition Operators ◽  
Dirichlet Space

Adjoints of linear fractional composition operators on the Dirichlet space

2003 ◽  
Vol 327 (1) ◽  
pp. 117-134 ◽  
Author(s):  
Eva A. Gallardo-Gutiérrez ◽  
Alfonso Montes-Rodríguez
Keyword(s):  
Fractional Composition ◽  
Composition Operators ◽  
Dirichlet Space

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.

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