A. Jabbari, Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran, e-mail: shahzadeh@math.um.ac.ir; M. S. Moslehian, Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran; Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Iran, e-mail: moslehian@ferdowsi.um.ac.ir and moslehian@ams.org; H. R. E. Vishki, Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran; Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Iran, e-mail: vishki@ferdowsi.um.ac.ir
Abstract: A surjective bounded homomorphism fails to preserve $n$-weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.
Keywords: weak amenability, $n$-weak amenability, derivation, second dual, direct sum, Banach algebra, Arens product
Classification (MSC 2000): 46H20, 46H25
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