Locally convex approach spaces
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Universitat Politècnica de València
2003-10-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/2031 |
| _version_ | 1811261509210210304 |
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| author | M. Sioen S. Verwulgen |
| author_facet | M. Sioen S. Verwulgen |
| author_sort | M. Sioen |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T19:05:21Z |
| format | Article |
| id | doaj.art-881d162bf32c4284b2d590ffef6c44ab |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-04-12T19:05:21Z |
| publishDate | 2003-10-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-881d162bf32c4284b2d590ffef6c44ab2022-12-22T03:20:02ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472003-10-014226327910.4995/agt.2003.20311648Locally convex approach spacesM. Sioen0S. Verwulgen1Vrije Universiteit BrusselUniversiteit AntwerpenWe 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.http://polipapers.upv.es/index.php/AGT/article/view/2031Approach vector spaceTopological vector spaceLocally convex spaceLocally convex approach spaceMinkowski functionalMinkowski systemProjective tensor product |
| spellingShingle | M. Sioen S. Verwulgen Locally convex approach spaces Applied General Topology Approach vector space Topological vector space Locally convex space Locally convex approach space Minkowski functional Minkowski system Projective tensor product |
| title | Locally convex approach spaces |
| title_full | Locally convex approach spaces |
| title_fullStr | Locally convex approach spaces |
| title_full_unstemmed | Locally convex approach spaces |
| title_short | Locally convex approach spaces |
| title_sort | locally convex approach spaces |
| topic | Approach vector space Topological vector space Locally convex space Locally convex approach space Minkowski functional Minkowski system Projective tensor product |
| url | http://polipapers.upv.es/index.php/AGT/article/view/2031 |
| work_keys_str_mv | AT msioen locallyconvexapproachspaces AT sverwulgen locallyconvexapproachspaces |