Fremlin Tensor Products of Concavifications of Banach Lattices

Abstract

Suppose that $E$ is a uniformly complete vector lattice and $p_1,...,p_n$ are positive reals. We prove that the diagonal of the Fremlin projective tensor product of $E_{(p_1)},...,E_{(p_n)}$ can be identified with $E_{(p)}$ where $p=p_1+...+p_n$ and $E_{(p)}$ stands for the $p$-concavification of $E$. We also provide a variant of this result for Banach lattices. This extends the main result of [BBPTT].

10 pages