A Schwarz lemma and composition operators

Files in This Item:
File Description SizeFormat 
schwarz.pdf290.17 kBAdobe PDFDownload
Title: A Schwarz lemma and composition operators
Authors: Mackey, Michael
Mellon, Pauline
Permanent link: http://hdl.handle.net/10197/6284
Date: Apr-2004
Abstract: We give an alternative description of the Carathéodory pseudodistance on a domain D in an arbitrary complex Banach space. This gives a Schwarz lemma for holomorphic maps of the domain.We specialise to the case of a bounded symmetric domain and obtain some applications. In particular, we give the connected components of the space of composition operators with symbol in a bounded symmetric domain. This generalises results for the space of composition operators on H∞(Δ) in [12] and for H∞(B) , B the unit ball of a Hilbert space or commutative C*-algebra in [2].
Type of material: Journal Article
Publisher: Springer
Copyright (published version): 2004 Birkhauser Verlag Basel/Switzerland
Keywords: Banach space;Schwarz lemma;Holomorphic maps;Hilbert space
DOI: 10.1007/s00020-003-1240-1
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

Show full item record

SCOPUSTM   
Citations 50

2
Last Week
0
Last month
checked on Jun 22, 2018

Google ScholarTM

Check

Altmetric


This item is available under the Attribution-NonCommercial-NoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. For other possible restrictions on use please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.