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Continuous Archimedean semigroups on real intervals

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Abstract

We study continuous Archimedean semigroups on real intervals. We give a complete description of them using real functions called ample functions. We give a criterion for two continuous Archimedean semigroups to be isomorphic in terms of their ample functions. Using this characterization we construct uncountably many non-isomorphic continuous Archimedean semigroups on a real interval.

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Authors and Affiliations

  1. Department of Information Science, Toho University, Funabashi, 274-8510, Japan

    Yuji Kobayashi, Sin-Ei Takahasi & Makoto Tsukada

Authors
  1. Yuji Kobayashi
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  2. Sin-Ei Takahasi
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  3. Makoto Tsukada
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Corresponding author

Correspondence to Makoto Tsukada.

Additional information

Communicated by Jimmie D. Lawson.

The authors were partially supported by JSPS Kakenhi Grand (C)-25400120.

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Kobayashi, Y., Takahasi, SE. & Tsukada, M. Continuous Archimedean semigroups on real intervals. Semigroup Forum 95, 159–178 (2017). https://doi.org/10.1007/s00233-017-9877-2

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  • DOI: https://doi.org/10.1007/s00233-017-9877-2

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