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A local spectral condition for strong compactness with some applications to bilateral weighted shifts

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Autor: Lacruz Martín, Miguel Benito
Romero de la Rosa, María del Pilar
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2014-01
Publicado en: Proceedings of the American Mathematical Society, 142 (1), 243-249.
Tipo de documento: Artículo
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 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.
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.
Tamaño: 112.0Kb
Formato: PDF

URI: http://hdl.handle.net/11441/44872

DOI: 10.1090/S0002-9939-2013-11764-8

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