<正>Inthispaper,westudycompositionoperatorsonaBanachspaceofanalyticfunctions,denotedbyX,whichincludestheBlochspace.ThisspacearisesnaturallyasthedualspaceofanalyticfunctionsintheBergmanspaceL_a~1(D)whichadmitanatomicdecomposition.Wecharac-terizethefunctionswhichinducecompactcompositionoperatorsandthosewhichinduceFredholmoperatorsonthisspace.Wealsoinvestigatewhenacompositionoperatorhasaclosedrange.