Daugavet Property in Tensor Product Spaces

Abstract

We study the Daugavet property in tensor products of Banach spaces. We show that L1(µ) ⊗ ε L1(ν) has the Daugavet property when µ and ν are purely non-atomic measures. Also, we show that X ⊗ π Y has the Daugavet property provided X and Y are L1-preduals with the Daugavet property, in particular spaces of continuous functions with this property. With the same tecniques, we also obtain consequences about roughness in projective tensor products as well as the Daugavet property of projective symmetric tensor products.2010 Mathematics Subject Classification. Primary 46B04; Secondary 46B20, 46B28.