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Bases and quasi‐reflexivity in Fréchet spaces
Author(s) -
Valdivia Manuel
Publication year - 2005
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.200310266
Subject(s) - mathematics , reflexivity , banach space , subspace topology , pure mathematics , countable set , space (punctuation) , product (mathematics) , fréchet space , reflexive space , interpolation space , mathematical analysis , functional analysis , geometry , sociology , linguistics , philosophy , social science , biochemistry , chemistry , gene
A Fréchet space E is quasi‐reflexive if, either dim( E ″/ E ) < ∞, or E ″[ β ( E ″, E ′)]/ E is isomorphic to ω . A Fréchet space E is totally quasi‐reflexive if every separated quotient is quasi‐reflexive. In this paper we show, using Schauder bases, that E is totally quasi‐reflexive if and only if it is isomorphic to a closed subspace of a countable product of quasi‐reflexive Banach spaces. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)