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Dense subspaces of quasinormable spaces
Author(s) -
Bonet José,
Dierolf Susanne,
Aye Aye Khin
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310386
Subject(s) - linear subspace , mathematics , banach space , countable set , characterization (materials science) , subspace topology , pure mathematics , regular polygon , locally convex topological vector space , fréchet space , discrete mathematics , interpolation space , functional analysis , mathematical analysis , topological space , geometry , biochemistry , chemistry , materials science , gene , nanotechnology
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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