On p-Compact Sets in Classical Banach Spaces
Given p ≥ 1, we denote by Cp the class of all Banach spaces X satisfying the equality Kp(Y,X) = Πdp(Y,X) for every Banach space Y , Kp (respectively, Πdp ) being the operator ideal of p-compact operators (respectively, of operators with p-summing adjoint). If X belongs to Cp, a bounded set A ⊂ X is...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2014 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/87528 |
| Acesso em linha: | https://hdl.handle.net/11441/87528 https://doi.org/10.12988/imf.2014.311215 |
| Access Level: | Acceso aberto |
| Palavra-chave: | p-compact set p-nuclear operator p-summing operator (p, q)- summing sequence |
| Resumo: | Given p ≥ 1, we denote by Cp the class of all Banach spaces X satisfying the equality Kp(Y,X) = Πdp(Y,X) for every Banach space Y , Kp (respectively, Πdp ) being the operator ideal of p-compact operators (respectively, of operators with p-summing adjoint). If X belongs to Cp, a bounded set A ⊂ X is relatively p-compact if and only if the evaluation map U∗ A : X∗ −→ ∞(A) is p-summing. We obtain p-compactness criteria valid for Banach spaces in Cp. |
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