A note on p-limited sets
Given p 1, a subset A of a Banach space X is said to be p-limited if for every weakly p-summable sequence (x∗ n) in X∗ there exists (αn) ∈ p such that | x∗ n, x | αn for all x ∈ A and n ∈ N. It is showed that p-limited sets are q-limited whenever p < q and Banach spaces enjoying the property that...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/163175 |
| Acceso en línea: | https://hdl.handle.net/11441/163175 https://doi.org/10.1016/j.jmaa.2013.08.045 |
| Access Level: | acceso abierto |
| Palabra clave: | p-Limited set p-Compact set p-Summing operator p-Compact operator Gelfand–Phillips property |
| Sumario: | Given p 1, a subset A of a Banach space X is said to be p-limited if for every weakly p-summable sequence (x∗ n) in X∗ there exists (αn) ∈ p such that | x∗ n, x | αn for all x ∈ A and n ∈ N. It is showed that p-limited sets are q-limited whenever p < q and Banach spaces enjoying the property that every q-limited subset is p-limited are characterized. We also prove that an operator has p-summing adjoint if and only if it maps relatively compact sets to p-limited sets. |
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