A topology on the Fremlin tensor product of locally convex-solid vector lattices

2024/05/11 by Zabeti, Omid
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2405.07073

Abstract

Suppose E and F are locally convex-solid vector lattices. Although we have a suitable vector lattice structure for the tensor product E and F (known as the Fremlin tensor product and denoted by E\otimesF), there is a lack of topological structure on E⊗ F, in general. In this note, we consider a topological attitude on E⊗ F that makes it into a locally convex-solid vector lattice, as well.

Related

• Order Continuous and Topological Representations of Archimedean Vector Lattices via S(X)-spaces
• Fremlin tensor product behaves well with the unbounded order convergence
• Complex Vector Lattices Via Functional Completions
• Fremlin Tensor Products of Concavifications of Banach Lattices
• Locally convex structures on higher local fields