On the topological centers of Banach algebras

ISSN: 1303-9709
Yayın Aralığı: Yıllık
Yayıncı: -

Let A be a Banach algebra with a bounded approximate identity. Let $Z_2$ and $widetilde{Z}_2$ be respectively, the topological centers of the algebras A** and (AA*)* with respect to the second Arens multiplication. In this paper, we show that $widetilde{M}_2$ is isometrically isomorphic to LM (A)> where $widetilde{M}_2$ is a closed subalgebra of $widetilde{Z}_2$ and LM(A) is the set of left multipliers operators of the Banach algebra A.

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1) Arens, R., ‘‘The adjoint of a bilinear operation’’, Proc. Amer. Math. Soc., 2, 839-848, (1951).
2) Hewitt, E. and Ross, K., ‘‘Abstract Harmonic Analysis’’, Volumes I and II, Newyork, (1970).
3) 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).
4) 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).
5) Lau, A.T. and Ülger, A., ‘‘Topological centers of certain dual algebras’’, Trans. Amer. Math. Soc., 348 (3), 1191-1212, (1996).