Bidual as a weak nonstandard hull

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dc.creatorNg, Siu-Ah
dc.date2008-10-17
dc.date.accessioned2026-07-07T10:10:56Z
dc.date.available2026-07-07T10:10:56Z
dc.descriptionWe construct the weak nonstandard hull of a normed linear space X from *X (the nonstandard extension of X) using the weak topology on X. The bidual (i.e. the second dual) X" is shown to be isometrically isomorphic to the weak nonstandard hull of X. Examples and applications to C*-algebras are given, including a simple proof of the Sherman-Takeda Theorem. As a consequence, the weak nonstandard hull of a C*-algebra is always a von Neumann algebra. Moreover a natural representation of the Arens product is given.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/0810.3090
dc.identifierhttp://arxiv.org/abs/0810.3090
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171740
dc.subjectFunctional Analysis
dc.subjectLogic
dc.subjectOperator Algebras
dc.subject46L05, 03H05, 26E3,5 46S20
dc.titleBidual as a weak nonstandard hull
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