Reference : DISTINGUISHEDNESS OF WEIGHTED FRECHET SPACES OF CONTINUOUS-FUNCTIONS
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/29460
DISTINGUISHEDNESS OF WEIGHTED FRECHET SPACES OF CONTINUOUS-FUNCTIONS
English
Bastin, Françoise mailto [Université de Liège - ULiège > Département de mathématique > Analyse, analyse fonctionnelle, ondelettes >]
1992
Proceedings of the Edinburgh Mathematical Society
Oxford Univ Press United Kingdom
35
Part 2
271-283
Yes (verified by ORBi)
International
0013-0915
1464-3839
Oxford
United Kingdom
[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.
http://hdl.handle.net/2268/29460
10.1017/S0013091500005538

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