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LIFTING DERIVATIONS AND n-WEAK AMENABILITY OF THE SECOND DUAL OF A BANACH ALGEBRA

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

Published online by Cambridge University Press:  26 November 2010

S. BAROOTKOOB  and
H. R. EBRAHIMI VISHKI
S. BAROOTKOOB
Affiliation:
Department of Pure Mathematics, Ferdowsi University of Mashhad, PO Box 1159, Mashhad 91775, Iran (email: sbk_923@yahoo.com)
H. R. EBRAHIMI VISHKI*
Affiliation:
Department of Pure Mathematics and Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, PO Box 1159, Mashhad 91775, Iran (email: vishki@um.ac.ir)
*
✉For correspondence; e-mail: vishki@um.ac.ir
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Abstract

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We show that for n≥2, n-weak amenability of the second dual 𝒜** of a Banach algebra 𝒜 implies that of 𝒜. We also provide a positive answer for the case n=1, which sharpens some older results. Our method of proof also provides a unified approach to give short proofs for some known results in the case where n=1.

Keywords

weak amenabilityn-weak amenabilityderivationsecond dualArens product

MSC classification

Secondary: 46H20: Structure, classification of topological algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 1 , February 2011 , pp. 122 - 129
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

This research was supported by a grant from Ferdowsi University of Mashhad (No. MP88107VIS).

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