Applications of semi-embeddings to the study of the projective tensor product of Banach spaces

Abstract

In this paper, we use the theory of semi-embeddings to show that if $E$ is a Banach lattice and $X$ is a Banach space then $E\,\hat{\otimes}\,X$, the projective tensor product of $E$ and $X$, has, respectively, the near Radon–Nikodym property, the analytic Radon–Nikodym property, the analytic complete continuity property, and the property of non-containment of a copy of $c_{0}$ whenever both $E$ and $X$ have the same property.