Lexicographic cones and the ordered projective tensor product

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Authors

Wortel, Marten

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Publisher

Springer

Abstract

We introduce lexicographic cones, a method of assigning an ordered vector space Lex(S) to a poset S, generalising the standard lexicographic cone. These lexicographic cones are then used to prove that the projective tensor cone of two arbitrary cones is a cone, and to find a new characterisation of finite-dimensional vector lattices.

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Keywords

Lexicographic cone, Finite-dimensional vector lattices, Ordered projective tensor product

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Citation

Wortel M. (2019) Lexicographic Cones and the Ordered Projective Tensor Product. In: Buskes G. et al. (eds) Positivity and Noncommutative Analysis. Trends in Mathematics. Birkhäuser, Cham.