Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T18:13:06.348Z Has data issue: false hasContentIssue false
  • English
  • Français

Corrigendum: amenability of ultrapowers of Banach algebras

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  16 August 2010

Matthew Daws
Matthew Daws
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK (matt.daws@cantab.net)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Some of the results of § 5 of the cited paper are incorrect: in particular, the characterization of when an algebra is ultra-amenable, in terms of a diagonal like construction, is not proved; and Theorem 5.7 is stated wrongly. The rest of the paper is unaffected. We shall show in this corrigendum that Theorem 5.7 can be corrected and that the other results of § 5 are true if the algebra in question has a certain approximation property.

Keywords

Banach algebraArens productsultrapoweramenabilitytensor product

MSC classification

Secondary: 46B08: Ultraproduct techniques in Banach space theory 46B28: Spaces of operators; tensor products; approximation properties
Type
Corrigenda
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 3 , October 2010 , pp. 633 - 637
Copyright
Copyright © Edinburgh Mathematical Society 2010

References

1. Blackadar, B., Operator algebras. Theory of C*-algebras and von Neumann algebras. (Springer, 2006).Google Scholar
2. Brown, M. and Ozawa, N., C*-algebras and finite-dimensional approximations (American Mathematical Society, Providence, RI, 2008).CrossRefGoogle Scholar
3. Daws, M., Amenability of ultrapowers of Banach algebras, Proc. Edinb. Math. Soc. 52(2009), 307–338.CrossRefGoogle Scholar
4. Daws, M. and Runde, V., Can B(lp) ever be amenable?, Studia Math. 188 (2005), 151–174.CrossRefGoogle Scholar
5. Dixmier, J., C*-algebras (North-Holland, Amsterdam, 1977).Google Scholar
6. Heinrich, S., Ultraproducts in Banach space theory, J. Reine Angew. Math. 313 (1980), 72–104.Google Scholar
7. Lau, A. T.-M., Loy, R. J. and Willis, G. A., Amenability of Banach and C*-algebras on locally compact groups, Studia Math. 119 (1996), 161–178.Google Scholar
8. Runde, V., Lectures on amenability (Springer, 2002).CrossRefGoogle Scholar
9. Ryan, R., Introduction to tensor products of Banach spaces (Springer, 2002).CrossRefGoogle Scholar