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 ωdϕd′, 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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Eberhardt, V. Über einen Graphensatz für Abbildungen mit normiertem Zielraum. Manuscripta Math 12, 47–65 (1974). https://doi.org/10.1007/BF01166233
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DOI: https://doi.org/10.1007/BF01166233