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ULTRAPOWERS OF BANACH ALGEBRAS AND MODULES

Published online by Cambridge University Press:  01 September 2008

MATTHEW DAWS
MATTHEW DAWS*
Affiliation:
School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK e-mail: matt.daws@cantab.net
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Abstract

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The Arens products are the standard way of extending the product from a Banach algebra to its bidual ″. Ultrapowers provide another method which is more symmetric, but one that in general will only give a bilinear map, which may not be associative. We show that if is Arens regular, then there is at least one way to use an ultrapower to recover the Arens product, a result previously known for C*-algebras. Our main tool is a principle of local reflexivity result for modules and algebras.

Keywords

46B0746B0846H0546H2546L05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 3 , September 2008 , pp. 539 - 555
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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