arXiv subjects

Chris Schwanke

Publications and source records attributed to Chris Schwanke.

2 recordsLinked to original sources

arXiv2014

Functional Completions of Archimedean Vector Lattices

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.

math.FA↗

arXiv2014

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.

math.FA↗