On the Topological Centers of Banach Algebras

Yıl 2006, Cilt: 19 Sayı: 1, 15 - 19, 24.03.2010

Hayri Akay Danyal Soybaş

Öz

Let A be a Banach algebra with a bounded approximate identity. Let  and be respectively, the topological centers of the algebras A** and (AA*)* with respect to the second Arens multiplication. In this paper, we show that is isometrically isomorphic to LM(A) , where  is a closed subalgebra of and LM(A) is the set of left multipliers operators of the Banach algebra A.

 

Key words: Topological center, Arens multiplication, Banach algebra, Left multiplier operator

 

Anahtar Kelimeler

Topological center, Arens multiplication, Banach algebra, Left multiplier operator

Kaynakça

• ) Arens, R., ‘‘The adjoint of a bilinear operation’’, Proc. Amer. Math. Soc., 2, 839-848, (1951).
• ) Hewitt, E. and Ross, K., ‘‘Abstract Harmonic Analysis’’, Volumes I and II, Newyork, (1970).
• ) Lau, A.T., ‘‘Continuity of Arens multiplication on the dual space of bounded uniformly continuous functions on locally compact groups and topological semigroups’’, Math. Proc. Camb. Philos. Soc., 99, 273-283, (1986).
• ) Lau, A.T. and Losert, V., ‘‘The C* algebra generated by operators with compact support on a locally compact group’’, J. Functinal Analysis, 112, 1-30, (1993).
• ) Lau, A.T. and Ülger, A., ‘‘Topological centers of certain dual algebras’’, Trans. Amer. Math. Soc., 348 (3), 1191-1212, (1996).