ULTRAPOWERS OF BANACH ALGEBRAS AND MODULES

DAWS, MATTHEW

Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 539-555

Résumé

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.

Détail

DOI : 10.1017/S0017089508004400

Mots-clés : 46B07, 46B08, 46H05, 46H25, 46L05

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