Three-space Problems for the Bounded Compact Approximation Property

(整期优先)网络出版时间:2013-04-14
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Inthispaper,thenotionoftheboundedcompactapproximationproperty(BCAP)ofapair[Banachspaceanditssubspace]isusedtoprovethatifXisaclosedsubspaceofL∞withtheBCAP,thenL∞/XhastheBCAP.WealsoshowthatX*hastheλ-BCAPwithconjugateoperatorsifandonlyifthepair(X,Y)hastheλ-BCAPforeachfinitecodimensionalsubspaceY∈X.LetMbeaclosedsubspaceofXsuchthatM⊥iscomplementedinX*.IfXhasthe(bounded)approximationpropertyoforderp,thenMhasthe(bounded)approximationpropertyoforderp.