Dense subspaces of quasinormable spaces
Identifieur interne : 001500 ( Main/Curation ); précédent : 001499; suivant : 001501Dense subspaces of quasinormable spaces
Auteurs : José Bonet [Espagne] ; Susanne Dierolf [Allemagne] ; Khin Aye Aye [Birmanie]Source :
- Mathematische Nachrichten [ 0025-584X ] ; 2006-05.
English descriptors
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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DOI: 10.1002/mana.200310386
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<front><div type="abstract" xml:lang="en">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)</div>
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