Bidual as a weak nonstandard hull
Functional Analysis
2008-10-20 v1 Logic
Operator Algebras
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.
Cite
@article{arxiv.0810.3090,
title = {Bidual as a weak nonstandard hull},
author = {Siu-Ah Ng},
journal= {arXiv preprint arXiv:0810.3090},
year = {2008}
}
Comments
14 pages