1. Functional completions of Archimedean vector lattices.
- Author
-
Buskes, Gerard and Schwanke, Christopher
- Subjects
ARCHIMEDEAN t-norm ,RIESZ spaces ,LATTICE theory ,HOMOGENEOUS polynomials ,FINITE element method - 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 mean 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. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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