1Mathematisch-Geographische Fakultät Universität Eichstätt – Ingolstadt Ostenstr. 26 D-85072 Eichstätt, Germany 2Departamento de Física y Matemática Aplicada Universidad de Navarra E-31080 Pamplona, Spain 3Departamento de Métodos Matemáticos y de Representación Universidad de A Coruña Campus de Elviña E-15071 A Coruña, Spain 4Muskhelishvili Institute of Computational Mathematics Georgian Academy of Sciences Tbilisi 0193, Georgia
Studia Mathematica, Tome 181 (2007) no. 3, pp. 199-210
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.
Keywords:
introduce notion schwartz group which turns out coherent known concept schwartz topological vector space establish several basic properties schwartz groups topological abelian groups locally convex spaces hemicompact k spaces schwartz groups prove every hemicompact k space topological group particular pontryagin dual metrizable topological group schwartz group
Affiliations des auteurs :
L. Außenhofer
1
;
M. J. Chasco
2
;
X. Domínguez
3
;
V. Tarieladze
4
1
Mathematisch-Geographische Fakultät Universität Eichstätt – Ingolstadt Ostenstr. 26 D-85072 Eichstätt, Germany
2
Departamento de Física y Matemática Aplicada Universidad de Navarra E-31080 Pamplona, Spain
3
Departamento de Métodos Matemáticos y de Representación Universidad de A Coruña Campus de Elviña E-15071 A Coruña, Spain
4
Muskhelishvili Institute of Computational Mathematics Georgian Academy of Sciences Tbilisi 0193, Georgia
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author = {L. Au{\ss}enhofer and M. J. Chasco and X. Dom{\'\i}nguez and V. Tarieladze},
title = {On {Schwartz} groups},
journal = {Studia Mathematica},
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year = {2007},
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doi = {10.4064/sm181-3-1},
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url = {http://geodesic.mathdoc.fr/articles/10.4064/sm181-3-1/}
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AU - M. J. Chasco
AU - X. Domínguez
AU - V. Tarieladze
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L. Außenhofer; M. J. Chasco; X. Domínguez; V. Tarieladze. On Schwartz groups. Studia Mathematica, Tome 181 (2007) no. 3, pp. 199-210. doi: 10.4064/sm181-3-1
