Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal
HTML articles powered by AMS MathViewer

by Volker Runde PDF
Trans. Amer. Math. Soc. 358 (2006), 391-402 Request permission

Abstract:

Let $G$ be a locally compact group, and let $\mathcal {WAP}(G)$ denote the space of weakly almost periodic functions on $G$. We show that, if $G$ is a $[\operatorname {SIN}]$-group, but not compact, then the dual Banach algebra $\mathcal {WAP}(G)^\ast$ does not have a normal, virtual diagonal. Consequently, whenever $G$ is an amenable, non-compact $[\operatorname {SIN}]$-group, $\mathcal {WAP}(G)^\ast$ is an example of a Connes-amenable, dual Banach algebra without a normal, virtual diagonal. On the other hand, there are amenable, non-compact, locally compact groups $G$ such that $\mathcal {WAP}(G)^\ast$ does have a normal, virtual diagonal.
References
Similar Articles
Additional Information
  • Volker Runde
  • Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
  • Email: vrunde@ualberta.ca
  • Received by editor(s): October 26, 2003
  • Received by editor(s) in revised form: June 1, 2004
  • Published electronically: July 26, 2005
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 391-402
  • MSC (2000): Primary 46H20; Secondary 22A15, 22A20, 43A07, 43A10, 43A60, 46H25, 46M18, 46M20
  • DOI: https://doi.org/10.1090/S0002-9947-05-03827-4
  • MathSciNet review: 2171239