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On p-Compact Sets in Classical Banach Spaces

 

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Author: Delgado Sánchez, Juan Manuel
Piñeiro Gómez, Cándido
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2014
Published in: International Mathematical Forum, 9 (2), 51-63.
Document type: Article
Abstract: 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.
Cite: Delgado Sánchez, J.M. y Piñeiro Gómez, C. (2014). On p-Compact Sets in Classical Banach Spaces. International Mathematical Forum, 9 (2), 51-63.
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URI: https://hdl.handle.net/11441/87528

DOI: 10.12988/imf.2014.311215

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