Banach spaces with the Daugavet property, and the centralizer

We introduce representable Banach spaces, and prove that the class R of such spaces satisfies the following properties: (1) Every member of R has the Daugavet property. (2) It Y is a member of R, then, for every Banach space X, both the space L(X, Y) (of all bounded linear operators from X to Y) and the complete injective tensor product X (circle times) over bar (epsilon) Y lie in R. (3)If K is a perfect compact Hausdorff topological space, then, for every Banach space Y, and for most vector space topologies tau on Y, the space C(K, (Y, tau)) (of all Y-valued tau-continuous functions on K) is a member of R. (4) If K is a perfect compact Hausdorff topological space, then, for every Banach space Y, most C(K, Y)superspaces (in the sense of [V. Kadets, N. Kalton, D. Werner, Remarks on rich subspaces of Banach spaces, Studia Math. 159 (2003) 195-206]) are members of R. (5) All dual Banach spaces without minimal M-summands are members of R. (c) 2007 Elsevier Inc. All rights reserved.