On a Generalization of the Spaces Introduced by M. De Wilde and Closed Graph Theorem

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概要

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• M. De Wilde defined in [1] certain types of linear topological spaces (in the sequel we suppose every linear topological space is Hausdorff) for which the closed graph theorem concerning linear mappings from Banach spaces is valid, i.e. the spaces with the reseau of type (P), (K), and (ε). In this paper we prove that all the types (P), (K), and (ε) coincide, consider a generalization of the spaces defined by M. De Wilde, and prove another type of closed graph theorem generalizing and simplifying the result obtained in [1], succeeding the investigation in the papers [2], [3], and [4].

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著者

• Nakamura Michiko

  Department Of Mathematics Faculty Of Science Science University Of Tokyo

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