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Dense subspaces of quasinormable spaces

✍ Scribed by José Bonet; Susanne Dierolf; Khin Aye Aye

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
120 KB
Volume
279
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Dense linear subspaces of quasinormable Fréchet spaces need not be quasinormable, as an example due to J. Bonet and S. Dierolf proved. A characterization of the quasinormability of dense linear subspaces of quasinormable locally convex spaces and several consequences are given. Moreover, an example of a dense linear subspace of a countable direct sum of Banach spaces, which is not quasinormable, is provided. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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