Reference : Diametral dimension(s) and prominent bounded sets
Scientific congresses and symposiums : Unpublished conference/Abstract
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/211982
Diametral dimension(s) and prominent bounded sets
English
Demeulenaere, Loïc mailto [Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes >]
20-Jun-2017
No
No
International
Septièmes journées Besançon-Neuchâtel d’analyse fonctionnelle
From June 20 to June 23, 2017
Besançon
France
[en] Diametral dimension ; Prominent bounded sets
[en] The classical diametral dimension (Bessaga, Mityagin, Pelczynski, Rolewicz), denoted by "Delta", is a topological invariant which can be used to characterize Schwartz and nuclear locally convex spaces. Mityagin also introduced a variant of this diametral dimension, denoted by "Delta_b", using bounded sets in its definition, contrary to "Delta". In this talk, we present some conditions assuring the equality of these two diametral dimensions for Fréchet spaces. Among these conditions, there is the notion of existence of prominent bounded sets, due to Terzioglu. In fact, it appears that the existence of prominent sets is implied by the property "Omega Bar" of Vogt and Wagner. Finally, we describe a construction which gives Schwartz and nuclear non-Fréchet spaces E verifying "Delta_b(E) = \Delta(E)".
Fonds pour la formation à la Recherche dans l'Industrie et dans l'Agriculture (Communauté française de Belgique) - FRIA
Researchers ; Professionals
http://hdl.handle.net/2268/211982
http://trimestres-lmb.univ-fcomte.fr/Septiemes-journees-Besancon.html

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