On (σ, τ)-module extension Banach algebras

الموضوعات :

M. Fozouni ¹ (Department of Mathematics, Gonbad Kavous University, P.O. Box 163, Gonbad-e Kavous, Golestan, Iran)

تاريخ الإرسال : 25 الأحد , ذو الحجة, 1435 تاريخ التأكيد : 09 الخميس , ربيع الثاني, 1436 تاريخ الإصدار : 09 الإثنين , صفر, 1436

الکلمات المفتاحية: derivation, Banach algebra, module extension, Ideal, Arens regular,

ملخص المقالة :

Let A be a Banach algebra and X be a Banach A-bimodule. In this paper, we define a new product on $A\oplus X$ and generalize the module extension Banach algebras. We obtain characterizations of Arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new Banach algebra.

المصادر:

[1] H. G. Dales, Banach Algebras and Automatic Continuity, Clarendon press, Oxford, 2000.

 

[2] H. G. Dales, F. Ghahramani, N. Gronbaek, Derivations into iterated duals of Banach algebras, Studia Math. 128(1). (1998), 19-54.

 

[4] F. F. Bonsall, J. Duncan, Complete Normed Algebras, Springer-Verlag, 1973.

 

[5] H. R. Ebrahimi-vishki, A. R. Khoddami, Character inner amenability of certain Banach algebras, Colloq. Math. 122. (2011) 225-232.

 

[6] M. Eshaghi Gordji, A. Niyazi Motlagh, Module Extension Banach Algebras and (; )-amenability, Eur. J. P. A. Math. Vol. 2, No. 3. (2009), 361-371.

 

[7] A. R. Medghalchi, H. Pourmahmood Aghababa, The first cohomology group of module extension Banach algebras, Rocky Mountain J. Math. Vol. 41. No. 5. (2011), 1639-1651.

 

[8] M. S. Moslehian, A. Niyazi Motlagh, Some note on (; )-amenability of Banach algebra, Studia Univ. Babes Bolyai, Math. Volume LIII, No. 3. (2008), 57-68.

 

[9] M. S. Monfared, On certain products of Banach algebras with applications to harmonic analysis, Studia Math. 178 (3). (2007), 277-294.

 

[10] K. H. Park, On derivations in noncommuattive semiprime rings and Banach algebras, Bull. Korean Math. Soc. 42. (2005), No. 4, 671-678.

 

[11] Y. Zhang, Weak amenability of module extensions of Banach algebras,Trans. Amer. Math. Soc. Vol. 354, No. 10. (2002), 4131-4151.