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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]
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Abstract

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. 

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