Minimal sets determining the topological centre of the algebra LUC(G)*

作者：Ferri Stefano^*; Neufang Matthias; Pachl Jan

来源：Bulletin of the London Mathematical Society, 2014, 46(5): 1043-1049.

DOI：10.1112/blms/bdu051

The study of the Banach algebra LUC(G)* associated to a topological group g has been of interest in abstract harmonic analysis. In particular, several a:tailors have studied the topological centre A(LUC(G)*) of this algebra, which is defined as the set of elements mu is an element of LUC(G)* such that left multiplication by mu is w* - w* -continuous. In recent Years, several Works have appeared in which it is shown that for a locally compact group g it is sufficient to test the continuity of I he left translation by mu, at just one specific point in order to determine whether mu is an element of LUC(G)* belongs to Lambda(LUC(G)*). In this work, we extend some of these results to a much larger class of groups which includes many non-locally compact groups as well as all the locally compact ones. This answers a question raised by Dales %26apos;Review of S. Ferri and M. Neufang, On the topological centre of the algebra LUC(G)* :for general topological groups%26apos;, J. Fund-. Anal. 144 (2007) 1 54-1 71. Amer. Math. Soc. MailSciNet Matheinatical Reviews, 2007]. We also obtain a corollary about the topological centre of any subsemigroup of fuggy containing the uniform compactification G(LUC) of hi particular, we shall prove that there are sets of just one point determining the topological centre of the uniform compactification

• 出版日期2014-10