scholarly journals Mean ergodic composition operators on spaces of holomorphic functions on a Banach space

2021 ◽  
Vol 500 (2) ◽  
pp. 125139
Author(s):  
David Jornet ◽  
Daniel Santacreu ◽  
Pablo Sevilla-Peris
Keyword(s):  
Banach Space ◽  
Composition Operators ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions

Composition operators on weighted spaces of holomorphic functions on the upper half plane

2018 ◽  
Vol 122 (1) ◽  
pp. 141
Author(s):  
Wolfgang Lusky
Keyword(s):  
Half Plane ◽  
Composition Operator ◽  
Unit Disc ◽  
Composition Operators ◽  
Bounded Operator ◽  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Weight Functions ◽  
Spaces Of Holomorphic Functions ◽  
Upper Half Plane

We consider moderately growing weight functions $v$ on the upper half plane $\mathbb G$ called normal weights which include the examples $(\mathrm{Im} w)^a$, $w \in \mathbb G$, for fixed $a > 0$. In contrast to the comparable, well-studied situation of normal weights on the unit disc here there are always unbounded composition operators $C_{\varphi }$ on the weighted spaces $Hv(\mathbb G)$. We characterize those holomorphic functions $\varphi \colon \mathbb G \rightarrow \mathbb G$ where the composition operator $C_{\varphi } $ is a bounded operator $Hv(\mathbb G) \rightarrow Hv(\mathbb G)$ by a simple property which depends only on $\varphi $ but not on $v$. Moreover we show that there are no compact composition operators $C_{\varphi }$ on $Hv(\mathbb G)$.

scholarly journals Mean ergodic composition operators on Banach spaces of holomorphic functions

2016 ◽  
Vol 270 (12) ◽  
pp. 4369-4385 ◽  
Author(s):  
María J. Beltrán-Meneu ◽  
M. Carmen Gómez-Collado ◽  
Enrique Jordá ◽  
David Jornet
Keyword(s):  
Banach Spaces ◽  
Composition Operators ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions

Li–Yorke chaos in linear dynamics

2014 ◽  
Vol 35 (6) ◽  
pp. 1723-1745 ◽  
Author(s):  
N. C. BERNARDES ◽  
A. BONILLA ◽  
V. MÜLLER ◽  
A. PERIS
Keyword(s):  
Composition Operators ◽  
Linear Manifold ◽  
Holomorphic Functions ◽  
Linear Operators ◽  
Fréchet Spaces ◽  
Linear Dynamics ◽  
Spaces Of Holomorphic Functions ◽  
Dense Set

We obtain new characterizations of Li–Yorke chaos for linear operators on Banach and Fréchet spaces. We also offer conditions under which an operator admits a dense set or linear manifold of irregular vectors. Some of our general results are applied to composition operators and adjoint multipliers on spaces of holomorphic functions.

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