Document Type: Research Paper


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


In this paper, we  study the Arens regularity properties of module actions. We investigate some properties of topological centers of module actions ${Z}^\ell_{B^{**}}(A^{**})$ and  ${Z}^\ell_{A^{**}}(B^{**})$ with some conclusions in group algebras.


Main Subjects

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

[2] J. Baker, A.T. Lau and J.S. Pym Module homomorphism and topological centers associated with weakly sequentially compact Banach algebras, Journal of Functional Analysis. 158 (1998), 186-208.

[3] F.F. Bonsall and J. Duncan, Complete normed algebras, Springer-Verlag, Berlin 1973.

[4] H.G. Dales, Banach algebra and automatic continuity, Oxford 2000.

[5] H.G. Dales, F. Ghahramani and N. Grnbk, Derivation into iterated duals of Banach algebras, Studia Math. 128 1 (1998), 19-53.

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

[7] E. Hewitt and K.A. Ross, Abstract harmonic analysis, Springer, Berlin, Vol I 1963.

[8] A.T. Lau and V. Losert, On the second Conjugate Algebra of locally compact groups, J. London Math. Soc. 37 (2)(1988), 464-480.

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

[10] S. Mohamadzadeh and H.R.E. Vishki, Arens regularity of module actions and the second adjoint of a derivation, Bulletin of the Australian Mathematical Society 77 (2008), 465-476.

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

[12] A. Ulger, Some stability properties of Arens regular bilinear operators, Proc. Amer. Math. Soc. (1991) 34, 443-454.

[13] A. Ulger, Arens regularity of weakly sequentialy complte Banach algebras, Proc. Amer. Math. Soc. 127 (11) (1999), 3221-3227.