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.

scholarly journals DIFFERENCES OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES AND WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONS

2010 ◽  
Vol 52 (2) ◽  
pp. 325-332 ◽  
Author(s):  
ELKE WOLF
Keyword(s):  
Banach Spaces ◽  
Unit Disk ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Holomorphic Functions ◽  
Weighted Bergman Spaces ◽  
Open Unit ◽  
Open Unit Disk ◽  
Spaces Of Holomorphic Functions ◽  
Weighted Banach Spaces

AbstractWe characterise boundedness and compactness of differences of composition operators acting between weighted Bergman spaces Av, p and weighted Banach spaces H∞w of holomorphic functions defined on the open unit disk D.

scholarly journals Multiplicative Isometries and Isometric Zero-Divisors

2010 ◽  
Vol 62 (5) ◽  
pp. 961-974 ◽  
Author(s):  
Alexandru Aleman ◽  
Peter Duren ◽  
María J. Martín ◽  
Dragan Vukotić
Keyword(s):  
Banach Spaces ◽  
Bloch Space ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Zero Divisors ◽  
Pointwise Multipliers ◽  
Type Spaces ◽  
Dirichlet Type Spaces ◽  
Coefficient Multipliers ◽  
Spaces Of Analytic Functions

AbstractFor some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated.

scholarly journals Volterra composition operators from generalized weighted weighted Bergman spaces toµ-Bloch spaces

2009 ◽  
Vol 7 (3) ◽  
pp. 225-240 ◽  
Author(s):  
Xiangling Zhu
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Bergman Space ◽  
Composition Operators ◽  
Bloch Space ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Bloch Spaces

Letφbe a holomorphic self-map andgbe a fixed holomorphic function on the unit ballB. The boundedness and compactness of the operatorTg,φf(z)=∫01f(φ(tz))ℜg(tz)dttfrom the generalized weighted Bergman space into the µ-Bloch space are studied in this paper.

scholarly journals Composition followed by differentiation between weighted Bergman spaces and weighted Banach spaces of holomorphic functions

2014 ◽  
Vol 6 (1) ◽  
pp. 107-116
Author(s):  
Elke Wolf
Keyword(s):  
Banach Spaces ◽  
Composition Operator ◽  
Bergman Spaces ◽  
Holomorphic Functions ◽  
Differentiation Operator ◽  
Weighted Bergman Spaces ◽  
Open Unit ◽  
Open Unit Disk ◽  
Spaces Of Holomorphic Functions ◽  
Weighted Banach Spaces

AbstractLet Φ be an analytic self-map of the open unit disk D in the complex plane. Such a map induces through composition a linear composition operator CΦ: f ↦ f◦Φ.We are interested in the combination of CΦwith the differentiation operator D, that is in the operator DCΦ: f ↦ Φ` · (f ◦ Φ) acting between weighted Bergman spaces and weighted Banach spaces of holomorphic functions

Sign in / Sign up

Export Citation Format

Share Document