Duality in spaces of operators and smooth norms on Banach spaces (Q1094627)

One gives a general representation for biduals of spaces of compact operators between reflexive Banach spaces, one shows how to lift the metric approximation property from a Banach space to its dual. An isomorphic version is obtained within the class of M-ideals. For a reflexive Banach space X, the space L(X) of continuous linear operators from X to X, equipped with the operator norm, has a unique isometric predual.