Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T02:42:39.378Z Has data issue: false hasContentIssue false
  • English
  • Français

ESSENTIAL AMENABILITY OF DUAL BANACH ALGEBRAS

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  24 May 2019

MOHSEN ZIAMANESH Open the ORCID record for MOHSEN ZIAMANESH [Opens in a new window] ,
BEHROUZ SHOJAEE Open the ORCID record for BEHROUZ SHOJAEE [Opens in a new window]  and
AMIN MAHMOODI Open the ORCID record for AMIN MAHMOODI [Opens in a new window]
MOHSEN ZIAMANESH
Affiliation:
Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran email [email protected]
BEHROUZ SHOJAEE
Affiliation:
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran email [email protected]
AMIN MAHMOODI*
Affiliation:
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran email [email protected]
*
✉[email protected]
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.

We show that an essentially amenable Banach algebra need not have an approximate identity. This answers a question posed by Ghahramani and Loy [‘Generalized notions of amenability’, J. Funct. Anal.  208 (2004), 229–260]. Essentially Connes-amenable dual Banach algebras are introduced and studied.

Keywords

Banach algebradual Banach algebraessential amenabilityessential Connes-amenability

MSC classification

Primary: 46H25: Normed modules and Banach modules, topological modules (if not placed in or )
Secondary: 46H20: Structure, classification of topological algebras 46H35: Topological algebras of operators
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 100 , Issue 3 , December 2019 , pp. 479 - 488
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

References

Dales, H. G., Lau, A. T. M. and Strauss, D., ‘Banach algebras on semigroups and their compactifications’, Mem. Amer. Math. Soc. 205(966) (2010), 1–165.Google Scholar
Ghahramani, F. and Loy, R. J., ‘Generalized notions of amenability’, J. Funct. Anal. 208 (2004), 229–260.Google Scholar
Johnson, B. E., ‘Cohomology in Banach algebras’, Mem. Amer. Math. Soc. 127 (1972), 1–96.Google Scholar
Kaniuth, E., Lau, A. T. and Pym, J., ‘On 𝜑-amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc. 144 (2008), 85–96.Google Scholar
Mahmoodi, A., ‘On 𝜑-Connes amenability of dual Banach algebras’, J. Linear Topol. Algebra 3 (2014), 211–217.Google Scholar
Mahmoodi, A., ‘Beurling and matrix algebras, (approximate) Connes-amenabilty’, U. P. B. Sci. Bull., Ser. A 78 (2016), 157–170.Google Scholar
Runde, V., ‘Amenability for dual Banach algebras’, Stud. Math. 148 (2001), 47–66.Google Scholar
Runde, V., Lectures on Amenability, Lecture Notes in Mathematics, Vol. 1774 (Springer, Berlin, 2002).Google Scholar
Runde, V., ‘Connes-amenability and normal virtual diagonals for measure alebras I’, J. Lond. Math. Soc. 67 (2003), 643–656.Google Scholar
Runde, V., ‘Dual Banach algebras: Connes-amenability, normal, virtual diagonal, and injectivity of the predual bimodule’, Math. Scand. 95 (2004), 124–144.Google Scholar
Samea, H., ‘Essential amenability of abstract segal algebras’, Bull. Aust. Math. Soc. 79 (2009), 319–325.Google Scholar
Sangani Monfared, M., ‘On certain products of Banach algebras with applications to harmonic analysis’, Stud. Math. 178 (2007), 277–294.Google Scholar