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Spaces of Linear and Bilinear Mappings

  • Gottfried Köthe
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 237)

Abstract

The set L (E, F) of all continuous linear mappings of E in F, where both E and F are locally convex, is a vector space. If F = K, then L (E, F) = E′ and so it is obvious that there are many possibilities to define a locally convex topology on L (E, F). This is done in § 39 and by adapting the methods of Volume I it is possible to obtain generalizations of some classical theorems as the Banach-Mackey theorem and the Banach-Steinhaus theorem. The relation between equicontinuous and weakly compact subsets of L (E, F) is a little more complicated than in the case of dual spaces.

Keywords

Approximation Property Convex Space Bilinear Mapping Finite Rank Closed Unit Ball 
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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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Gottfried Köthe
    • 1
  1. 1.Institut für Angewandte MathematikJohann-Wolfgang-Goethe UniversitätFrankfurt am MainFederal Republic of Germany

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