Title
Locally convex approach spacesLocally convex approach spaces
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Faculty of Design Sciences
Publication type
article
Publication
Subject
Mathematics
Source (journal)
Applied General Topology
Volume/pages
4(2003):2, p. 263-279
ISSN
1576-9402
Carrier
E
Target language
English (eng)
Abstract
We continue the investigation of suitable structures for quantified functional analysis, by looking at the notion of local convexity in the setting of approach vector spaces as introduced in [6]. We prove that the locally convex objects are exactly the ones generated (in the usual approach sense) by collections of seminorms. Furthermore, we construct a quantified version of the projective tensor product and show that the locally convex objects admitting a decent exponential law with respect to it are precisely the seminormed spaces.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/93f628/471be1f0.pdf