Czechoslovak Mathematical Journal, first online, pp. 1-13


Character Connes amenability of dual Banach algebras

Mohammad Ramezanpour

Received August 23, 2016.   First published January 18, 2018.

Abstract:  We study the notion of character Connes amenability of dual Banach algebras and show that if $A$ is an Arens regular Banach algebra, then $A^{**}$ is character Connes amenable if and only if $A$ is character amenable, which will resolve positively Runde's problem for this concept of amenability. We then characterize character Connes amenability of various dual Banach algebras related to locally compact groups. We also investigate character Connes amenability of Lau product and module extension of Banach algebras. These help us to give examples of dual Banach algebras which are not Connes amenable.
Keywords:  dual Banach algebra; Connes amenability; character amenability; locally compact group
Classification MSC:  46H20, 46H25, 43A07, 22D15
DOI:  10.21136/CMJ.2018.0451-16

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Affiliations:   Mohammad Ramezanpour, School of Mathematics and Computer Science, Damghan University, P. O. Box 36716, Damghan 41167, Iran, e-mail: ramezanpour@du.ac.ir, md_ramezanpour@yahoo.com


 
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