Document Type: Research Paper


Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.


We introduce  the weak topological centers of left and right module actions and we study some of their properties.  We investigate the relationship between these new concepts and the  topological centers of of left and right module actions with some results in the group algebras.


Main Subjects

[1] R.E. Arens,  The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951) 839-848.

[2] H.G. Dales, A. Rodrigues-Palacios, and M.V. Velasco, The second transpose of a derivation, J. London. Math. Soc.  64 (2001) 707-721.

[3] M. Eshaghi Gordji and  M. Filali, Arens regularity of module actions,  Studia Math. 181 (2007)  237-254.

[4] K. Haghnejad Azar, Arens regularity of bilinear forms and unital Banach module space, Bull. Iranian Math. Soc, 40  (2014) 505-520.

[5] K. Haghnejad Azar, A. Bodaghi, and A. Jabbari, Some notes on the topological centers of module actions, Iranian Journal of Science and Technology. IJST (2015) 417-431.

[6] A.T. Lau and  V. Losert, On the second Conjugate Algebra of locally compact groups, J. London Math. Soc. 37 (1988) 464-480.

[7] A.T. Lau and   A. Ülger, Topological center of certain dual algebras, Trans. Amer.  Math. Soc. 348 (1996) 1191-1212.

[8] S. Mohamadzadih and   H.R.E. Vishki, Arens regularity of module actions and the second adjoint of a derivation, Bull. Aust Math Soc. 77 (2008) 465-476.

[9] J.S. Pym, The convolution of functionals on spaces of bounded functions, Proc. London Math Soc. 15 (1965) 84-104.

[10] Y. Zhang, Weak amenability of module extentions of Banach algebras, Trans. Amer. Math. Soc. 354 (2002) 4131-4151.