Abstract
In the present paper it is shown that if S1 and S2 are two Clifford topological semigroups satisfying certain conditions and T is an isometric isomorphism of LUC(S1*) onto LUC(S2*), then T maps S1 topologically isomorphically onto S2. Furthermore, T maps Ml n(S1) (M(S1), respectively) isometrically isomorphically onto Ml n(S2) (M(S2), respectively). Indeed, we have obtained a generalization of a well-known result of Ghahramani, Lau and Losert for locally compact groups to a more general setting of Clifford topological semigroups.
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Bami, M. Isometric Isomorphisms Between Banach Algebras Related to a Certain Class of Clifford Topological Semigroups. Semigroup Forum 69, 219–229 (2004). https://doi.org/10.1007/s00233-004-0106-4
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DOI: https://doi.org/10.1007/s00233-004-0106-4