Thin and thick sets in locally convex spaces

Yilmaz, Yimaz

doi:10.1016/j.na.2006.07.028

Thin and thick sets in locally convex spaces

Atıf İçin Kopyala

Yilmaz Y.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, cilt.67, sa.5, ss.1440-1444, 2007 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 67 Sayı: 5
Basım Tarihi: 2007
Doi Numarası: 10.1016/j.na.2006.07.028
Dergi Adı: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.1440-1444
İnönü Üniversitesi Adresli: Hayır

Özet

We introduce in this work some normed space notions such as norming, thin and thick sets in general locally convex spaces. We also study some effects of thick sets on the uniform boundedness-like principles in locally convex spaces such as "weak*-bounded sets are strong*-bounded if and only if the space is a Banach-Mackey space". It is proved that these principles occur under some weaker conditions by means of thick sets. Further, we show that the thickness is a duality invariant, that is, all compatible topologies for some locally convex space have the same thick sets. (C) 2006 Elsevier Ltd. All rights reserved.