Ultrapowers of Banach algebras and modules
نویسنده
چکیده
The Arens products are the standard way of extending the product from a Banach algebra A to its bidual A′′. 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 A 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. 2000 Mathematics Subject Classification: 46B07, 46B08, 46H05, 46H25, 46L05
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