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DISTINGUISHEDNESS OF WEIGHTED FRECHET SPACES OF CONTINUOUS-FUNCTIONS
Bastin, Françoise
1992In Proceedings of the Edinburgh Mathematical Society, 35 (Part 2), p. 271-283
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Abstract :
[en] In this paper, we prove that if U is an increasing sequence of strictly positive and continuous functions on a locally compact Hausdorff space X such that VBAR congruent-to VBAR and C(X), then the Frechet space CU(X) is distinguished if and only if it satisfies Heinrich's density condition, or equivalently, if and only if the sequence U satisfies condition (H) (cf. e.g.`[1] for the introduction of (H)). As a consequence, the bidual lambda(infinity)(A) of the distinguished Kothe echelon space lambda-0(A) is distinguished if and only if the space lambda-1(A) is distinguished. This gives counterexamples to a problem of Grothendieck in the context of Kothe echelon spaces.
Disciplines :
Mathematics
Author, co-author :
Bastin, Françoise ;  Université de Liège - ULiège > Département de mathématique > Analyse, analyse fonctionnelle, ondelettes
Language :
English
Title :
DISTINGUISHEDNESS OF WEIGHTED FRECHET SPACES OF CONTINUOUS-FUNCTIONS
Publication date :
1992
Journal title :
Proceedings of the Edinburgh Mathematical Society
ISSN :
0013-0915
eISSN :
1464-3839
Publisher :
Oxford Univ Press United Kingdom, Oxford, United Kingdom
Volume :
35
Issue :
Part 2
Pages :
271-283
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 25 November 2009

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