Daugavet points in projective tensor products

Abstract

In this paper, we are interested in studying when an element z in the projective tensor product X ⊗ π Y turns out to be a Daugavet point. We prove first that, under some hypothesis, the assumption of X ⊗ π Y having the Daugavet property implies the existence of a great amount of isometries from Y into X * . Having this in mind, we provide methods for constructing non-trivial Daugavet points in X ⊗ π Y . We show that C(K)-spaces are examples of Banach spaces such that the set of the Daugavet points in C(K) ⊗ π Y is weakly dense when Y is a subspace of C(K) * . Finally, we present some natural results on when an elementary tensor x ⊗ y is a Daugavet point.