dc.contributor.author De Jeu, Marcel dc.contributor.author Messerschmidt, Miek dc.date.accessioned 2016-02-15T07:20:00Z dc.date.available 2016-02-15T07:20:00Z dc.date.issued 2014 dc.identifier.citation De 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.issn 0001-8707 dc.identifier.issn 1090-2082 (Online) dc.identifier.uri http://hdl.handle.net/10394/16288 dc.description.abstract We show that a continuous additive positively homogeneous map en_US 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. dc.description.sponsorship Vrije Competitie grant of the Netherlands Organisation fo rScientific Research (NWO) en_US dc.description.uri http://www.journals.elsevier.com/advances-in-mathematics/ dc.language.iso en en_US dc.publisher Elsevier en_US dc.subject Cone en_US dc.subject open mapping theorem en_US dc.subject Banach space en_US dc.subject bounded continuous right inverse en_US dc.subject ordered Banach space en_US dc.title A strong open mapping theorem for surjections from cones onto Banach spaces en_US dc.type Article en_US
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