[Banach] Abstract of a paper by Siu-Ah Ng

This is an announcement for the paper "Bidual as a weak nonstandard hull" by Siu-Ah Ng.

Abstract: We 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.

Archive classification: math.FA math.LO math.OA

Mathematics Subject Classification: 46L05, 03H05, 26E3,5 46S20

Remarks: 14 pages

The source file(s), bidual.tex: 38768 bytes, is(are) stored in gzipped form as 0810.3090.gz with size 11kb. The corresponding postcript file has gzipped size 87kb.

Submitted from: ngs@ukzn.ac.za

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