Bishop operators: invariant subspaces and spectral theory
For nearly a century, various classes of linear bounded operators have been posed as potential counter examples to the Invariant Subspace Problem: maybe, the most important long-standing open question in Operator Theory. One of the simplest candidates consists of the family of Bishop operators T act...
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| Formato: | tesis doctoral |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/11570 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/11570 |
| Access Level: | acceso abierto |
| Palavra-chave: | 517.98(043.2) Operators Theory Teoría de operadores Análisis funcional y teoría de operadores |
| Resumo: | For nearly a century, various classes of linear bounded operators have been posed as potential counter examples to the Invariant Subspace Problem: maybe, the most important long-standing open question in Operator Theory. One of the simplest candidates consists of the family of Bishop operators T acting on Lp [0; 1) spaces, which were suggested by Errett Bishop in the fifties. Unlike their seeming simplicity, the structure and features of Bishop operators remain largely uncharted. In particular, hitherto, it is still unknown whether T has non-trivial invariant subspaces in Lp [0; 1) for each 1 p < 1 and any irrational 2 (0; 1)... |
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