On Schwartz groups

Volume 181 / 2007

L. Außenhofer, M. J. Chasco, X. Domínguez, V. Tarieladze Studia Mathematica 181 (2007), 199-210 MSC: 22A05, 46A11. DOI: 10.4064/sm181-3-1


We introduce a notion of a Schwartz group, which turns out to be coherent with the well known concept of a Schwartz topological vector space. We establish several basic properties of Schwartz groups and show that free topological Abelian groups, as well as free locally convex spaces, over hemicompact $k$-spaces are Schwartz groups. We also prove that every hemicompact $k$-space topological group, in particular the Pontryagin dual of a metrizable topological group, is a Schwartz group.


  • L. AußenhoferMathematisch-Geographische Fakultät
    Universität Eichstätt – Ingolstadt
    Ostenstr. 26
    D-85072 Eichstätt, Germany
  • M. J. ChascoDepartamento de Física
    y Matemática Aplicada
    Universidad de Navarra
    E-31080 Pamplona, Spain
  • X. DomínguezDepartamento de Métodos Matemáticos
    y de Representación
    Universidad de A Coruña
    Campus de Elviña
    E-15071 A Coruña, Spain
  • V. TarieladzeMuskhelishvili Institute
    of Computational Mathematics
    Georgian Academy of Sciences
    Tbilisi 0193, Georgia

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