Complex Vector Lattices Via Functional Completions

2014/10/21 by Gerard Buskes, Buskes, Gerard, Chris Schwanke +1
Mathematics · #46A40 #46B40 #4GG25 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46A40 #msc:46B40 #msc:4GG25

paper · pdf · doi:10.48550/arxiv.1410.5881

arxiv created 2014/10/21 · arxiv updated 2014/10/23

Abstract

We show that the Fremlin tensor product C(X)⊗C(Y) is not square mean complete when X and Y are uncountable metrizable compact spaces. This motivates the definition of complexification of Archimedean vector lattices, the Fremlin tensor product of Archimedean complex vector lattices, and a theory of powers of Archimedean complex vector lattices.

Related

• Functional Completions of Archimedean Vector Lattices
• Tensor Products of Archimedean Riesz Spaces: a Representational Approach
• Fremlin tensor product behaves well with the unbounded order convergence
• Order Continuous and Topological Representations of Archimedean Vector Lattices via S(X)-spaces
• Two Results on Fremlin's Archimedean Riesz Space Tensor Product