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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.

preprint2014arXivOpen access
Gerard BuskesChris Schwanke
math.FA
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Open access2 authors1 topic
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Gerard BuskesChris Schwanke

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