A topology on the Fremlin tensor product between locally solid vector lattices

Abstract

Let $E$ and $F$ be locally solid vector lattices. In this short note, we establish a locally solid topology on the Fremlin tensor product $E\overline{\otimes}F$ and we denote it by $\tau_{E\overline{\otimes}F}$. It extends the Fremlin projective tensor product in the setting of Banach lattices. We show that $\tau_{E\overline{\otimes}F}$ is Hausdorff provided that both $E$ and $F$ are Hausdorff.