[en] The diametral dimension is a topological invariant which characterizes Schwartz and
nuclear spaces. However, there exists another diametral dimension which was conjectured
by Bessaga, Mityagin, Pełczynski, and Rolewicz to be equal to the first one in
Fréchet spaces.
In this talk, we describe some conditions which assure the equality of the two diametral
dimensions in metrizable locally convex spaces. Besides, we explain why such an
equality is generally impossible in non-metrizable spaces.
Disciplines :
Mathematics
Author, co-author :
Demeulenaere, Loïc ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes