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Lexicographic Cones and the Ordered Projective Tensor Product

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Positivity and Noncommutative Analysis

Part of the book series: Trends in Mathematics ((TM))

Abstract

We introduce lexicographic cones, a method of assigning an ordered vector space \( \operatorname {\mathrm {Lex}}(S)\) 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.

Dedicated to Ben de Pagter on the occasion of his 65th birthday

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa

    Marten Wortel

Authors
  1. Marten Wortel
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Correspondence to Marten Wortel .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Mississippi, Oxford, MS, USA

    Gerard Buskes

  2. Mathematical Institute, Leiden University, Leiden, The Netherlands; Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa

    Marcel de Jeu

  3. College of Science and Engineering, Flinders University, Adelaide, Australia

    Peter Dodds

  4. Department of Mathematics, University of South Carolina, Columbia, SC, USA

    Anton Schep

  5. School of Mathematics and Statistics, University of New South Wales, Sydney, Australia

    Fedor Sukochev

  6. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Jan van Neerven

  7. Mathematical Sciences Research Centre, Queen’s University Belfast, Belfast, UK

    Anthony Wickstead

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Wortel, M. (2019). Lexicographic Cones and the Ordered Projective Tensor Product. In: Buskes, G., et al. Positivity and Noncommutative Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-10850-2_30

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