AN EQUIVARIANT VERSION OF THE HAHN-BANACH THEOREM

DC FieldValueLanguage
dc.contributor.authorSCHMITT, LM
dc.date.accessioned2021-12-23T15:57:48Z-
dc.date.available2021-12-23T15:57:48Z-
dc.date.issued1992
dc.identifier.issn03621588
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/3138-
dc.description.abstractWe prove an equivariant version of the Hahn-Banach Theorem, that allows simultaneous access to Day's [DAY 1] versions of the Hahn-Banach Theorem and the Krein-Rutman Extension Theorem [K&R 1] as well as related Theorems due to Wittstock [WIT 1] and Arveson [ARV 1]. We discuss an order-theoretical characterization of injective, unital C*-algebras. It can be used to get simple proofs of stability properties of injective W*-algebras. Our main application is the proof of a conjecture by Silverman [SIL 1]: Let (L, L+) be an ordered vector space with the least upper bound property. Suppose that S is a right amenable, discrete semigroup acting identically on L. If V is a real vector space with a representation of S as linear operators on V, and theta : V --> L is a sublinear map satisfying theta . sigma less-than-or-equal-to theta, sigma is-an-element of S, then there exists an S-equivariant, linear map theta : V --> L satisfying phi less-than-or-equal-to theta. In particular a discrete semigroup S is right amenable if and only if a S-equivariant Hahn-Banach principle for the real numbers is valid.
dc.language.isoen
dc.publisherUNIV HOUSTON
dc.relation.ispartofHOUSTON JOURNAL OF MATHEMATICS
dc.subjectMathematics
dc.subjectSPACES
dc.subjectW-STAR-ALGEBRAS
dc.titleAN EQUIVARIANT VERSION OF THE HAHN-BANACH THEOREM
dc.typejournal article
dc.identifier.isiISI:A1992JQ54700011
dc.description.volume18
dc.description.issue3
dc.description.startpage429
dc.description.endpage447
dc.publisher.placeDEPT MATH, HOUSTON, TX 77204
dcterms.isPartOf.abbreviationHoust. J. Math.
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