A Schwarz lemma and composition operators
|Title:||A Schwarz lemma and composition operators||Authors:||Mackey, Michael
|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  and for H∞(B) , B the unit ball of a Hilbert space or commutative C*-algebra in .||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:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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