Stampacchia's Property, Self-duality and Orthogonality Relations

Yannakakis, N

dc.contributor.author	Yannakakis, N	en
dc.date.accessioned	2014-03-01T01:37:07Z
dc.date.available	2014-03-01T01:37:07Z
dc.date.issued	2011	en
dc.identifier.issn	1877-0533	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21453
dc.subject	Coercive operator	en
dc.subject	Cosine of a linear operator	en
dc.subject	Hilbert space characterization	en
dc.subject	Orthogonality relation	en
dc.subject	Positive operator	en
dc.subject	Self-dual Banach space	en
dc.subject.other	VARIATIONAL-INEQUALITIES	en
dc.subject.other	BANACH-SPACES	en
dc.subject.other	OPERATORS	en
dc.subject.other	MONOTONE	en
dc.title	Stampacchia's Property, Self-duality and Orthogonality Relations	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s11228-011-0175-y	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s11228-011-0175-y	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	We show that if the conclusion of the well known Stampacchia Theorem on variational inequalities holds on a real Banach space X, then X is isomorphic to a Hilbert space. Motivated by this, we obtain a relevant result concerning self-dual Banach spaces and investigate some connections between properties of orthogonality relations, self-duality and Hilbert space structure. Moreover, we revisit the notion of the cosine of a linear operator and show that it can be used to characterize real Banach spaces that are isomorphic to a Hilbert space. Finally, we present some consequences of our results to quadratic forms and to evolution triples. © 2011 Springer Science+Business Media B.V.	en
heal.publisher	SPRINGER	en
heal.journalName	Set-Valued and Variational Analysis	en
dc.identifier.doi	10.1007/s11228-011-0175-y	en
dc.identifier.isi	ISI:000295143700003	en
dc.identifier.volume	19	en
dc.identifier.issue	4	en
dc.identifier.spage	555	en
dc.identifier.epage	567	en