Faces and renormings of ℓ1
The faces of the unit ball of a finite-dimensional Banach space are automatically closed. The situation is different in the infinite-dimensional case. In fact, under this last condition, the closure of a face may not be a face. In this paper, we discuss these issues in an expository style. In order...
| Main Authors: | , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
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MDPI
2023
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10835/14184 |
| _version_ | 1789406635184095232 |
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| author | Navarro Pascual, Juan Carlos Zarauz Moreno, Antonio |
| author_facet | Navarro Pascual, Juan Carlos Zarauz Moreno, Antonio |
| author_sort | Navarro Pascual, Juan Carlos |
| collection | DSpace |
| description | The faces of the unit ball of a finite-dimensional Banach space are automatically closed. The situation is different in the infinite-dimensional case. In fact, under this last condition, the closure of a face may not be a face. In this paper, we discuss these issues in an expository style. In order to illustrate the described situation we consider an equivalent renorming of the Banach space ℓ1. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-14184 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2023 |
| publisher | MDPI |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-141842023-04-12T19:39:10Z Faces and renormings of ℓ1 Navarro Pascual, Juan Carlos Zarauz Moreno, Antonio convex set face of a convex set equivalent renorming of a Banach space The faces of the unit ball of a finite-dimensional Banach space are automatically closed. The situation is different in the infinite-dimensional case. In fact, under this last condition, the closure of a face may not be a face. In this paper, we discuss these issues in an expository style. In order to illustrate the described situation we consider an equivalent renorming of the Banach space ℓ1. 2023-01-26T07:27:46Z 2023-01-26T07:27:46Z 2022-12-29 info:eu-repo/semantics/article 2227-7390 http://hdl.handle.net/10835/14184 10.3390/math11010193 en https://www.mdpi.com/2227-7390/11/1/193 Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess MDPI |
| spellingShingle | convex set face of a convex set equivalent renorming of a Banach space Navarro Pascual, Juan Carlos Zarauz Moreno, Antonio Faces and renormings of ℓ1 |
| title | Faces and renormings of ℓ1 |
| title_full | Faces and renormings of ℓ1 |
| title_fullStr | Faces and renormings of ℓ1 |
| title_full_unstemmed | Faces and renormings of ℓ1 |
| title_short | Faces and renormings of ℓ1 |
| title_sort | faces and renormings of ℓ1 |
| topic | convex set face of a convex set equivalent renorming of a Banach space |
| url | http://hdl.handle.net/10835/14184 |
| work_keys_str_mv | AT navarropascualjuancarlos facesandrenormingsofl1 AT zarauzmorenoantonio facesandrenormingsofl1 |