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Locally Convex Spaces. Fundamentals

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Part of the Grundlehren der mathematischen Wissenschaften book series (GL,volume 159)

Abstract

The first two paragraphs are concerned with methods of producing new locally convex spaces from given ones. Thus subspaces and quotient spaces of locally convex spaces are again locally convex. The same holds for topological products and locally convex direct sums. The completion of a locally convex space is obtained in a simple way by embedding the space in a topological product of Banach spaces.

Keywords

  • Weak Topology
  • Dual Pair
  • Convex Space
  • Topological Product
  • Strong Topology

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1983 Springer-Verlag Berlin, Heidelberg

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Köthe, G. (1983). Locally Convex Spaces. Fundamentals. In: Topological Vector Spaces I. Grundlehren der mathematischen Wissenschaften, vol 159. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-64988-2_4

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  • DOI: https://doi.org/10.1007/978-3-642-64988-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64990-5

  • Online ISBN: 978-3-642-64988-2

  • eBook Packages: Springer Book Archive