Fremlin Tensor Products of Concavifications of Banach Lattices

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