Über einen Graphensatz für Abbildungen mit normiertem Zielraum |
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Authors: | Volker Eberhardt |
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Institution: | 1. Mathematisches Institut der Universit?t München, Theresienstr. 39, D 8000, München 2
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Abstract: | This paper contains a detailed study of those locally convex spaces E-which we call GN-spaces-for which the following closed graph theorem holds: Every closed linear map from E to any normed linear space is continuous. In the first two sections we establish some characterisations and permanence-properties of these spaces. The main result reads as follows: Every separated GN-space is isomorphic to a barrelled subspace of some ωd?d′, and conversely. Then we determine those GN-spaces which are (DF)-spaces, Schwartz-spaces or nuclear spaces. Finally we show that neither the strong dual nor the tensor product of GN-spaces are GN-spaces. |
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