SOME QUESTIONS OF HEINRICH ON ULTRAPOWERS OF LOCALLY CONVEX-SPACES

Authors
Citation
A. Galbis et A. Peris, SOME QUESTIONS OF HEINRICH ON ULTRAPOWERS OF LOCALLY CONVEX-SPACES, Mathematische Nachrichten, 161, 1993, pp. 271-282
Citations number
22
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
ISSN journal
0025584X
Volume
161
Year of publication
1993
Pages
271 - 282
Database
ISI
SICI code
0025-584X(1993)161:<271:SQOHOU>2.0.ZU;2-8
Abstract
In this note we treat some open problems of HEINRICH on ultrapowers of locally convex spaces. In section 1 we investigate the localization o f bounded sets in the full ultrapower of a locally convex space, in pa rticular the coincidence of the full and the bounded ultrapower, mainl y concentrating in the case of (DF)-spaces. In section 2 we provide a partial answer to a question of HEINRICH on commutativity of strict in ductive limits and ultrapowers. In section 3 we analyze the relation b etween some natural candidates for the notion of superreflexivity in t he setting of Frechet spaces. We give an example of a Frechet-Schwartz space which is not the projective limit of a sequence of superreflexi ve Banach spaces.