Power-regular Bishop operators and spectral decompositions
It is proved that a wide class of Bishop-type operators $T_{\phi,\tau}$ are power-regular operators in $L^p(\Omega, \mu)$, $1 \leq p < \infty$, computing the exact value of the local spectral radius at any function $u \in L^p(\Omega, \mu)$. Moreover, it is shown that the local spectral radius at...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/129352 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/129352 |
| Access Level: | acceso abierto |
| Palabra clave: | Bishop operators Decomposable operators Power-regular operators Análisis funcional y teoría de operadores 1202.03 Álgebra y Espacios de Banach 1202.14 Espacio de Hilbert |
| Sumario: | It is proved that a wide class of Bishop-type operators $T_{\phi,\tau}$ are power-regular operators in $L^p(\Omega, \mu)$, $1 \leq p < \infty$, computing the exact value of the local spectral radius at any function $u \in L^p(\Omega, \mu)$. Moreover, it is shown that the local spectral radius at any $u$ coincides with the spectral radius of $T_{\phi,\tau}$ as far as u is non-zero. As a consequence, it is proved that non-invertible Bishop-type operators are non-decomposable whenever $\log|\phi| \in L^1(\Omega, \mu)$ (in particular, not quasinilpotent); not enjoying even the weaker spectral decompositions Bishop property $(\beta)$ and property $(\delta)$. |
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