Cándido Piñeiro Gómez

Juan Manuel Delgado Sánchez

English

Delgado Sánchez, Juan Manuel

Piñeiro Gómez, Cándido

idUS. Depósito de Investigación Universidad de Sevilla

A CHARACTERIZATION OF OPERATORS WITHp-SUMMING ADJOINT VIA p-LIMITED SETSJUAN MANUEL DELGADO AND CÁNDIDO PIÑEIROA subset A of a Banach space X is limited if and only if for everyweak∗ null sequence (x∗n) in X∗ there exists a sequence (αn) ∈ c0 suchthat |〈x∗n, x〉| ≤ αn for all x ∈ A and n ∈ N. As an extension ofthis notion, a subset A of a Banach space X is said to be p-limited(p ∈ [1,∞)) if for every weakly p-summable sequence (x∗n) in X∗ thereexists (αn) ∈ `p such that |〈x∗n, x〉| ≤ αn for all x ∈ A and n ∈ N [2].Some basic properties related to this notion are showed as well as itsconnections with (different forms of) compactness. As an application,we give a characterization of operators with p-summing adjoint as thosemapping relatively compact sets to p-limited sets.The research was supported by MTM2009-14483-C02-01 and MTM2012-36740-C02-01 projects (Spain).References[1] J. M. Delgado and C. Piñeiro, A note on p-limited sets. preprint.[2] A. K. Karn and D. P. Sinha, An operator summability in sequences inBanach spaces, arXiv:1207.3620 [math.FA] (2012).Higher Technical School of Architecture, University of Seville,41012 Seville, Av. Reina Mercedes, 2, SpainE-mail address: jmdelga@us.esFaculty of Experimental Sciences, University of Huelva, 21071 Huelva,Campus Universitario de El Carmen, SpainE-mail address: candido@uhu.es1

A characterization of operators with p-summing adjoint via p-limited sets

https://idus.us.es/bitstream/11441/96403/1/Delgado-Tartu_2013%28abs%29.pdf

A characterization of operators with p-summing adjoint via p-limited sets

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idUS. Depósito de Investigación Universidad de Sevilla