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On the Order Dual of a Riesz Space

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Discrete Mathematics and Theoretical Computer Science (DMTCS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2731))

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Abstract

The order-bounded linear functionals on a Rieszs pace are investigated constructively. Two classically equivalent notions of positivity for linear functionals, and their relation to the strong extensionality, are examined. A necessary and sufficient condition for the existence of the supremum of two elements of the order dual of a Rieszs pace with unit is obtained.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand

    Marian Alexandru Baroni

Authors
  1. Marian Alexandru Baroni
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Auckland, Maths-Physics Building 303, 38 Princes St., Auckland, New Zealand

    Cristian S. Calude  & Michael J. Dinneen  & 

  2. Université de Bourgogne, LE2I, B.P. 47870, 21078, Dijon Cedex, France

    Vincent Vajnovszki

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© 2003 Springer-Verlag Berlin Heidelberg

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Baroni, M.A. (2003). On the Order Dual of a Riesz Space. In: Calude, C.S., Dinneen, M.J., Vajnovszki, V. (eds) Discrete Mathematics and Theoretical Computer Science. DMTCS 2003. Lecture Notes in Computer Science, vol 2731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45066-1_8

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  • DOI: https://doi.org/10.1007/3-540-45066-1_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40505-4

  • Online ISBN: 978-3-540-45066-5

  • eBook Packages: Springer Book Archive

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