This is an announcement for the paper "Functional completions of archimedean vector lattices" by Gerard Buskes and Chris Schwanke.
Abstract: We study completions of Archimedean vector lattices relative to any nonempty set of positively-homogeneous functions on finite-dimensional real vector spaces. Examples of such completions include square mean closed and geometric closed vector lattices, amongst others. These functional completions also lead to a universal definition of the complexification of any Archimedean vector lattice and a theory of tensor products and powers of complex vector lattices in a companion paper.
Archive classification: math.FA
Mathematics Subject Classification: 06F20, 46A40
Submitted from: mmbuskes@olemiss.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.5878
or