English

Complex Vector Lattices Via Functional Completions

Functional Analysis 2014-10-23 v1

Abstract

We show that the Fremlin tensor product C(X)ˉC(Y)C(X)\bar{\otimes}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.

Keywords

Cite

@article{arxiv.1410.5881,
  title  = {Complex Vector Lattices Via Functional Completions},
  author = {Gerard Buskes and Chris Schwanke},
  journal= {arXiv preprint arXiv:1410.5881},
  year   = {2014}
}
R2 v1 2026-06-22T06:32:03.722Z