Artículo
A local spectral condition for strong compactness with some applications to bilateral weighted shifts
Autor/es | Lacruz Martín, Miguel Benito
Romero de la Rosa, María del Pilar |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2014-01 |
Fecha de depósito | 2016-09-09 |
Publicado en |
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Resumen | An algebra of bounded linear operators on a Banach space is said to be
strongly compact if its unit ball is precompact in the strong operator topology, and a bounded linear operator on a Banach space is said to be strongly ... An algebra of bounded linear operators on a Banach space is said to be strongly compact if its unit ball is precompact in the strong operator topology, and a bounded linear operator on a Banach space is said to be strongly compact if the algebra with identity generated by the operator is strongly compact. Our interest in this notion stems from the work of Lomonosov on the existence of invariant subspaces. We provide a local spectral condition that is sufficient for a bounded linear operator on a Banach space to be strongly compact. This condition is then applied to describe a large class of strongly compact, injective bilateral weighted shifts on Hilbert spaces, extending earlier work of Fernández-Valles and the first author. Further applications are also derived, for instance, a strongly compact, invertible bilateral weighted shift is constructed in such a way that its inverse fails to be a strongly compact operator. |
Agencias financiadoras | Ministerio de Ciencia e Innovación (MICIN). España Junta de Andalucía |
Identificador del proyecto | MTM 2009-08934
FQM-3737 |
Cita | Lacruz Martín, M.B. y Romero de la Rosa, M.d.P. (2014). A local spectral condition for strong compactness with some applications to bilateral weighted shifts. Proceedings of the American Mathematical Society, 142 (1), 243-249. |
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