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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Detalhes bibliográficos
Autor: Monsalve López, Miguel
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
Descrição
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)...