Complex Vector Lattices Via Functional Completions
  We show that the Fremlin tensor product $C(X)\bar{\otimes}C(Y)$ 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. 
Gerard Buskes and Chris Schwanke
math.FA