A Bishop-Phelps-Bollobas Type Theorem for uniform algegras
This paper is devoted to showing that Asplund operators with range in a uniform Banach algebra have the Bishop¿Phelps¿Bollobas property, i.e., they are approximated by norm attaining Asplund operators at the same time that a point where the approximated operator almost attains its norm is approximat...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/37716 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/37716 |
| Access Level: | acceso abierto |
| Palabra clave: | Bishop-Phelps-Bollobás Asplund operators Norm attaining Uniform Banach algebra Peak functions Urysohn lemma IUMPA MATEMATICA APLICADA |
| Sumario: | This paper is devoted to showing that Asplund operators with range in a uniform Banach algebra have the Bishop¿Phelps¿Bollobas property, i.e., they are approximated by norm attaining Asplund operators at the same time that a point where the approximated operator almost attains its norm is approximated by a point at which the approximating operator attains it. To prove this result we use the weak*-to-norm fragmentability of weak*-compact subsets of the dual of Asplund spaces and we need to observe a Urysohn type result producing peak complex-valued functions in uniform algebras that are small outside a given open set and whose image is inside a Stolz region. |
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