Article (Scientific journals)
Diametral dimensions of Fréchet spaces
Demeulenaere, Loïc; Frerick, Leonhard; Wengenroth, Jochen
2016In Studia Mathematica, 234 (3), p. 271-280
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Keywords :
Fréchet spaces; Diametral dimension; Prominent sets
Abstract :
[en] This article provides new results concerning the equality between two diametral dimensions. It shows that this equality is true for hilbertizable Fréchet-Schwartz spaces. Moreover, it studies the notion of prominent sets of Terzioglu and proves that the property "omega bar" of Vogt and Wagner implies the existence of prominent sets. Finally, it shows that the converse implication is true for regular Köthe sequence spaces and brings some spaces with prominent sets but which do not verify “omega bar” (among which there is the space H(D) x H(C)).
Disciplines :
Mathematics
Author, co-author :
Demeulenaere, Loïc  ;  Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Frerick, Leonhard;  Universität Trier > FB IV - Mathematik > Analysis
Wengenroth, Jochen;  Universität Trier > FB IV - Mathematik > Funktionalanalysis
Language :
English
Title :
Diametral dimensions of Fréchet spaces
Publication date :
2016
Journal title :
Studia Mathematica
ISSN :
0039-3223
eISSN :
1730-6337
Publisher :
Polish Academy of Science, Warszawa, Poland
Volume :
234
Issue :
3
Pages :
271-280
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
FRIA - Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture [BE]
Commentary :
The document here enclosed is the "Online First" version of the article.
Available on ORBi :
since 21 June 2016

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