An approximation property related to $M$-ideals of compact operators

Rafael Pay{á, Wend Werner
1991 Proceedings of the American Mathematical Society  
We investigate a variant of the compact metric approximation property which, for subspaces X of c0 , is known to be equivalent to K(X), the space of compact operators on X , being an A/-ideal in the space of bounded operators on X , L{X). Among other things, it is shown that an arbitrary Banach space X has this property iff K(Y, X) is an Af-ideal in L(Y, X) for all Banach spaces Y and, furthermore, that X must contain a copy of c0 . The proof of the central theorem of this note uses a
more » ... zation of those Banach spaces X for which K(X) is an Af-ideal in L(X) obtained earlier by the second author, as well as some techniques from Banach algebra theory.
doi:10.1090/s0002-9939-1991-1039261-1 fatcat:tmifeafxdnamte5vbirejhl3ji