Arens regularity and local reflexivity principle for Banach algebras
type: Item
instance of: scholarly article
title: Arens regularity and local reflexivity principle for Banach algebras
zbMATH Open document ID: 0648.46044
DOI: 10.1007/BF01443502
author: G. Loupias
author: Bruno Iochum
published in: Mathematische Annalen
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164537
review text: Let E be a non necessarily associative Banach algebra. Using ultraproduct techniques, we define on \(E^{**}\) a product \(_{(J^ 0,{\mathcal U})}\) depending on some ultrafilter \({\mathcal U}\) and extending the original one on E. Though generally different from the Arens products, it coincides with them (and E is Arens regular) if it is separately \(w^ *\)-continuous. Automorphisms, antiautomorphisms and multipliers on E extend to \((E^{**},_{(J^ 0,{\mathcal U})})\). We give some criteria for the associativity of \(_{(J^ 0,{\mathcal U})}\). Finally we associate to each \(_{(J^ 0,{\mathcal U})}\) a topology on \(E^{**}\), and compare it with the Mackey topology.
Mathematics Subject Classification ID: 46H05
Mathematics Subject Classification ID: 46H70
zbMATH DE Number: 4058200
zbMATH Keywords: ultraproduct techniques
zbMATH Keywords: ultrafilter
zbMATH Keywords: Arens products
zbMATH Keywords: Mackey topology
zbMATH Keywords: Arens regularity
zbMATH Keywords: local reflexivity principle
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4058200