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...

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Detalhes bibliográficos
Autores: Delgado Sánchez, Juan Manuel, Piñeiro Gómez, Cándido
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
Descrição
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.