Abstract
Let S be a semitopological semgroup and let Cb (S) denote the B*-algebra of all continuous bounded complex-valued functions on S. In this paper, we consider a left m-introverted and translation invariant B*-subalgebra F of Cb(S) containing the constant functions. Our concern is with ΔF, the maximal ideal space of F up to an isomorphic homeomorphism, when it is made into a compact right topological semigroup containing a dense continous homomorphic image of S under the Gelfand topology and a suitably chosen binary operation. We establish a representation of the closed left ideals of ΔF and study its centre and ideal structure in some special cases.
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