Joint continuity of multiplication on the dual of the left uniformly continuous functions |
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Authors: | Pekka Salmi |
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Institution: | (1) Department of Mathematics, Semnan University, Semnan, Iran |
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Abstract: | Let G be a locally compact group and LUC(G) the C*-algebra of the bounded left uniformly continuous functions on G. The spectrum G
LUC of LUC(G) is the universal semigroup compactification of G with respect to the joint continuity property: the multiplication on G×G
LUC is jointly continuous. The paper studies the joint weak* continuity of multiplication on LUC(G)* and, in particular, the question how the joint continuity property of G
LUC can be related to a property concerning the whole algebra LUC(G)*. The group G is naturally replaced by the measure algebra M(G), and LUC(G)* can be identified with M(G
LUC), the space of regular Borel measures on G
LUC. It is shown that the joint weak* continuity can fail even on bounded sets of M(G)×M(G
LUC), but, on the other hand, the multiplication on M(G)×M(G
LUC) is positive continuous in the sense of Jewett. |
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Keywords: | |
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