UEB-Topology on the Norm-Strict Bidual of Banach Algebras

For a Banach algebra A the strict topology on A is defined as the locally convex topology on A induced by the family of seminorms f a; a 2 Ag, where a(b) = kabk, for all b 2 A. By the norm-strict bidual of A we mean the norm dual of the space (A; ) . In this paper, among other things, we investigate the continuity properties of the product on ((A; ) ; k k) , for some special Banach algebras. In particular, generalizing some results of M. Neufang, we show that if B is a norm bounded subset of < A A > , and if m0 2 RM(A), the right multiplier algebra of A, and n0 2 B, then the mapping (m; n) ! m n from < A A > B into < A A > is jointly continuous at (m0; n0) in the UEB- topology, that is the topology ofuniform convergence on equicontinuous bounded subsets of < A A > .

کلیدواژه ها:

Equicontinuous set ، strict topology ، bounded approximate identity ، norm-strict bidual ، UEB-topology