Premium
Some Questions of Heinrich on Ultrapowers of Locally Convex Spaces
Author(s) -
Galbis Antonio,
Peris Alfredo
Publication year - 1993
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19931610120
Subject(s) - ultraproduct , mathematics , section (typography) , pure mathematics , bounded function , interpolation space , fréchet space , banach space , direct limit , limit of a sequence , locally convex topological vector space , reflexive space , limit (mathematics) , functional analysis , mathematical analysis , topological space , computer science , biochemistry , chemistry , gene , operating system
In this note we treat some open problems of Heinrich on ultrapowers of locally convex spaces. In section 1 we investigate the localization of bounded sets in the full ultrapower of a locally convex space, in particular the coincidence of the full and the bounded ultrapower, mainly concentrating in the case of ( DF )‐spaces. In section 2 we provide a partial answer to a question of Heinrich on commutativity of strict inductive limits and ultrapowers. In section 3 we analyze the relation between some natural candidates for the notion of superreflexivity in the setting of Fréchet spaces. We give an example of a Fréchet‐Schwartz space which is not the projective limit of a sequence of superreflexive Banach spaces.