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Stability in locally L0-convex modules and a conditional version of James' compactness theorem

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dc.contributor.authorOrihuela Calatayud, José
dc.contributor.authorZapata García, José Miguel
dc.contributor.departmentEstadística e Investigación Operativa
dc.date.accessioned2025-01-26T10:02:05Z
dc.date.available2025-01-26T10:02:05Z
dc.date.issued2017-03-23
dc.description© 2017 Elsevier Inc. All rights reserved. This document is the Published version of a Published Work that appeared in final form in Journal of Mathematical Analysis and Applications. To access the final edited and published work see https://doi.org/10.1016/j.jmaa.2017.03.048
dc.description.abstractLocally L0-convex modules were introduced in Filipovic et al. (2009) [10] as the analytic basis for the study of conditional risk measures. Later, the algebra of conditional sets was introduced in Drapeau et al. (2016) [8]. In this paper we study locally L0-convex modules, and find exactly which subclass of locally L0-convex modules can be identified with the class of locally convex vector spaces within the context of conditional set theory. Second, we provide a version of the classical James’ theorem of characterization of weak compactness for conditional Banach spaces. Finally, we state a conditional version of the Fatou and Lebesgue properties for conditional convex risk measures and, as application of the developed theory, we establish a version of the so-called Jouini–Schachermayer–Touzi theorem for robust representation of conditional convex risk measures defined on a L∞-type module.
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dc.identifier.citationJ. Math. Anal. Appl. 452 (2017) 1101–1127
dc.identifier.doihttps://doi.org/10.1016/j.jmaa.2017.03.048
dc.identifier.issnPrint: 0022-247X
dc.identifier.issnElectronic: 1096-0813
dc.identifier.urihttp://hdl.handle.net/10201/149289
dc.languageenges
dc.publisherElsevier
dc.relationPartially supported by Ministerio de Economía y Competitividad and FEDER project MTM2014-57838-C2-1-P; and Fundación Séneca CARM, project 19368/PI/14. The second author was partially supported by the grant MINECO MTM2014-57838-C2-1-P.es
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S0022247X17302998?via%3Dihub
dc.rights.accessRightsinfo:eu-repo/semantics/restrictedAccess
dc.subjectStability properties
dc.subjectLocally L0-convex module
dc.subjectConditionally locally convex space
dc.subjectJames’ compactness theorem
dc.subjectJouini–Schachermayer–Touzi
dc.subjectTheorem
dc.titleStability in locally L0-convex modules and a conditional version of James' compactness theoremes
dc.typeinfo:eu-repo/semantics/articlees
dspace.entity.typePublicationes
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Stability in Locally L0-Convex Modules and a Conditional Version of James' Compactness Theorem
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