University of Mohaghegh Ardabili Journal of Hyperstructures 2251-8436 1 2 2012 12 01 Lw∗wc and Rw∗wc and weak amenability of banach algebras 61 70 2548 10.22098/jhs.2012.2548 EN K. Haghnejad Azar Department of Mathematics and Applications, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, P.O. Box 56199-11367, Ardabil, Iran. Z. Ranjbar Department of Mathematics and Applications, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, P.O. Box 56199-11367, Ardabil, Iran. Journal Article 2012 04 03 We introduce some new concepts as lef t − weak∗ − weak convergence property [Lw∗wc−property] and right−weak∗− weak convergence property [Rw∗wc−property] for Banach algebra A. Suppose that A ∗ and A ∗∗, respectively, have Rw∗wc−property and Lw∗wc−property, then if A ∗∗ is weakly amenable, it follows that A is weakly amenable. Let D : A → A ∗ be a surjective derivation. If D 00 is a derivation, then A is Arens regular. Amenability weak amenability derivation Arens regularity Topological centers Module actions Lef t − weak∗ − to − weak convergence https://jhs.uma.ac.ir/article_2548_fa8ed25521d04fb42f92af395137d412.pdf