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Functional completions of Archimedean vector lattices

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.

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Correspondence to Gerard Buskes.

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Buskes, G., Schwanke, C. Functional completions of Archimedean vector lattices. Algebra Univers. 76, 53–69 (2016). https://doi.org/10.1007/s00012-016-0386-z

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2010 Mathematics Subject Classification

  • Primary: 46A40
  • Secondary: 06F20

Keywords and phrases

  • vector lattices
  • functional calculus
  • functional completions
  • convex functions