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Duality in spaces of operators and smooth norms on Banach spaces. (English) Zbl 0631.46015
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.

46B20 Geometry and structure of normed linear spaces
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces