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A Schwarz lemma and composition operators
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A Schwarz lemma and composition operators
Author(s)
Mackey, Michael
Mellon, Pauline
Uri
http://hdl.handle.net/10197/6284
Date Issued
2004-04
Date Available
2015-01-13T11:06:17Z
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
Journal
Integral Equations and Operator Theory
Volume
48
Issue
4
Start Page
511
End Page
524
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
English
Status of Item
Peer reviewed
This item is made available under a Creative Commons License
https://creativecommons.org/licenses/by-nc-nd/3.0/ie/
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schwarz.pdf
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