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dc.contributor.authorDe Jeu, Marcel
dc.contributor.authorMesserschmidt, Miek
dc.date.accessioned2016-02-15T07:20:00Z
dc.date.available2016-02-15T07:20:00Z
dc.date.issued2014
dc.identifier.citationDe Jeu, M. & Messerschmidt, M. 2014. A strong open mapping theorem for surjections from cones onto Banach spaces. Advances in mathematics, 259(10):43-86. [http://www.journals.elsevier.com/advances-in-mathematics/]en_US
dc.identifier.issn0001-8707
dc.identifier.issn1090-2082 (Online)
dc.identifier.urihttp://hdl.handle.net/10394/16288
dc.description.abstractWe show that a continuous additive positively homogeneous map from a closed not necessarily proper cone in a Banach space onto a Banach space is an open map precisely when it is surjective. This generalization of the usual Open Mapping Theorem for Banach spaces is then combined with Michael’s Selection Theorem to yield the existence of a continuous bounded positively homogeneous right inverse of such a surjective map; a strong version of the usual Open Mapping Theorem is then a special case. As another consequence, an improved version of the analogue of Andô’s Theorem for an ordered Banach space is obtained for a Banach space that is, more generally than in Andô’s Theorem, a sum of possibly uncountably many closed not necessarily proper cones. Applications are given for a (pre)-ordered Banach space and for various spaces of continuous functions taking values in such a Banach space or, more generally, taking values in an arbitrary Banach space that is a finite sum of closed not necessarily proper cones.en_US
dc.description.sponsorshipVrije Competitie grant of the Netherlands Organisation fo rScientific Research (NWO)en_US
dc.description.urihttp://www.journals.elsevier.com/advances-in-mathematics/
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.subjectConeen_US
dc.subjectopen mapping theoremen_US
dc.subjectBanach spaceen_US
dc.subjectbounded continuous right inverseen_US
dc.subjectordered Banach spaceen_US
dc.titleA strong open mapping theorem for surjections from cones onto Banach spacesen_US
dc.typeArticleen_US


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