The canonical partial metric and the uniform convexity on normed spaces
In this paper we introduce the notion of canonical partial metric associated to a norm to study geometric properties of normed spaces. In particular, we characterize strict convexity and uniform convexity of normed spaces in terms of the canonical partial metric defined by its norm. We prove that...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2005-10-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/1954 |
| _version_ | 1818308017925390336 |
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| author | S. Oltra Salvador Romaguera E.A. Sánchez-Pérez |
| author_facet | S. Oltra Salvador Romaguera E.A. Sánchez-Pérez |
| author_sort | S. Oltra |
| collection | DOAJ |
| description | In this paper we introduce the notion of canonical partial metric associated to a norm to study geometric properties of normed spaces. In particular, we characterize strict convexity and uniform convexity of normed spaces in terms of the canonical partial metric defined by its norm.
We prove that these geometric properties can be considered, in this sense, as topological properties that appear when we compare the natural metric topology of the space with the non translation invariant topology induced by the canonical partial metric in the normed space. |
| first_indexed | 2024-12-13T07:07:35Z |
| format | Article |
| id | doaj.art-0a940a7a29ef40fdae8a6c5b8e34bdad |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-13T07:07:35Z |
| publishDate | 2005-10-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-0a940a7a29ef40fdae8a6c5b8e34bdad2022-12-21T23:55:46ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472005-10-016218519410.4995/agt.2005.19541579The canonical partial metric and the uniform convexity on normed spacesS. Oltra0Salvador Romaguera1E.A. Sánchez-Pérez2Universitat Politècnica de ValènciaUniversitat Politècnica de ValènciaUniversitat Politècnica de ValènciaIn this paper we introduce the notion of canonical partial metric associated to a norm to study geometric properties of normed spaces. In particular, we characterize strict convexity and uniform convexity of normed spaces in terms of the canonical partial metric defined by its norm. We prove that these geometric properties can be considered, in this sense, as topological properties that appear when we compare the natural metric topology of the space with the non translation invariant topology induced by the canonical partial metric in the normed space.http://polipapers.upv.es/index.php/AGT/article/view/1954Partial metricConvexityNormed spaces |
| spellingShingle | S. Oltra Salvador Romaguera E.A. Sánchez-Pérez The canonical partial metric and the uniform convexity on normed spaces Applied General Topology Partial metric Convexity Normed spaces |
| title | The canonical partial metric and the uniform convexity on normed spaces |
| title_full | The canonical partial metric and the uniform convexity on normed spaces |
| title_fullStr | The canonical partial metric and the uniform convexity on normed spaces |
| title_full_unstemmed | The canonical partial metric and the uniform convexity on normed spaces |
| title_short | The canonical partial metric and the uniform convexity on normed spaces |
| title_sort | canonical partial metric and the uniform convexity on normed spaces |
| topic | Partial metric Convexity Normed spaces |
| url | http://polipapers.upv.es/index.php/AGT/article/view/1954 |
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