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Algebra universalis

, Volume 76, Issue 1, pp 53–69 | Cite as

Functional completions of Archimedean vector lattices

  • Gerard BuskesEmail author
  • Christopher Schwanke
Article

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.

Keywords and phrases

vector lattices functional calculus functional completions convex functions 

2010 Mathematics Subject Classification

Primary: 46A40 Secondary: 06F20 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MississippiMississippiUSA
  2. 2.Unit for BMINorth-West UniversityPotchefstroomSouth Africa

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