Schwartz groups and convergence of characters |
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Authors: | MJ Chasco X Domínguez V Tarieladze |
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Institution: | a Dept. de Física y Matemática Aplicada, Universidad de Navarra, Spain b Dept. de Métodos Matemáticos y de Representación, Universidad de A Coruña, Spain c Niko Muskhelishvili Institute of Computational Mathematics, Tbilisi, Georgia |
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Abstract: | It is proved that a locally quasi-convex group is a Schwartz group if and only if every continuously convergent filter on its dual group converges locally uniformly. We also show that for metrizable separable groups a similar result remains true when filters are replaced by sequences. As an ingredient in the proofs of these results, we obtain a Schauder-type theorem on compact homomorphisms acting between the natural group analogues of normed spaces. |
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Keywords: | 22A05 54A20 46A11 |
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