Fremlin Tensor Products of Concavifications of Banach Lattices

TL;DR

This paper investigates the structure of Fremlin tensor products of p-concavified Banach lattices, establishing an identification of the diagonal with a higher concavification, extending previous results in the field.

Contribution

It proves that the diagonal of the Fremlin tensor product of p-concavified Banach lattices can be identified with a higher concavification, generalizing earlier work.

Findings

Diagonal of tensor product identified with p-concavification

Extension of previous results to Banach lattices

Provides a variant for 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].