A Schwarz lemma and composition operators

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Title: A Schwarz lemma and composition operators
Authors: Mackey, Michael
Mellon, Pauline
Permanent link: http://hdl.handle.net/10197/6284
Date: Apr-2004
Online since: 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 spaceSchwarz lemmaHolomorphic mapsHilbert space
DOI: 10.1007/s00020-003-1240-1
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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