The 2-concavification of a Banach lattice equals the diagonal of the Fremlin tensor square

TL;DR

This paper explores the connection between the diagonal of the Fremlin tensor product of a Banach lattice and its 2-concavification, revealing a fundamental equivalence.

Contribution

It establishes that the 2-concavification of a Banach lattice equals the diagonal of its Fremlin tensor square, providing new insights into tensor product structures.

Findings

The 2-concavification and the diagonal of the tensor square are equivalent.

New characterization of Banach lattice structures via tensor products.

Enhanced understanding of tensorial properties in Banach lattices.

Abstract

We investigate the relationship between the diagonal of the Fremlin projective tensor product of a Banach lattice $E$ with itself and the 2-concavification of $E$.