Mackey, MichaelMichaelMackeyMellon, PaulinePaulineMellon2015-01-132015-01-132004 Birk2004-04Integral Equations and Operator Theoryhttp://hdl.handle.net/10197/6284We 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].enThe final publication is available at www.springerlink.comBanach spaceSchwarz lemmaHolomorphic mapsHilbert spaceJournal Article48451152410.1007/s00020-003-1240-12014-12-10https://creativecommons.org/licenses/by-nc-nd/3.0/ie/