Delgado Sánchez, Juan ManuelPiñeiro, C.2024-10-012024-10-012014Delgado Sánchez, J.M. y Piñeiro, C. (2014). A note on p-limited sets. Journal Of Mathematical Analysis and Applications, 410 (2), 713-718. https://doi.org/10.1016/j.jmaa.2013.08.045.0022-247X1096-0813https://hdl.handle.net/11441/163175Given 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.application/pdf6 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/p-Limited setp-Compact setp-Summing operatorp-Compact operatorGelfand–Phillips propertyinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1016/j.jmaa.2013.08.045