On Schwartz groups

• Autorzy: L. Außenhofer , M. J. Chasco , X. Domínguez , V. Tarieladze
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46A11: Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
• 22A05: Structure of general topological groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 181
• Numer: 3
• Strony: 199-210

Daty

wydano

2007

Twórcy

autor

L. Außenhofer

• Mathematisch-Geographische Fakultät, Universität Eichstätt - Ingolstadt, Ostenstr. 26, D-85072 Eichstätt, Germany

autor

M. J. Chasco

• Departamento de Física y Matemática Aplicada, Universidad de Navarra, E-31080 Pamplona, Spain

autor

X. Domínguez

• Departamento de Métodos Matemáticos y de Representación, Universidad de A Coruña, Campus de Elviña, E-15071 A Coruña, Spain

autor

V. Tarieladze

• Muskhelishvili Institute of Computational Mathematics, Georgian Academy of Sciences, Tbilisi 0193, Georgia

Identyfikatory

DOI

10.4064/sm181-3-1