Abstract
A net in the group algebra of a locally compact group which commutes asymptotically with elements from the measure algebra is called quasi-central. In this paper we provide new characterizations of locally compact groups whose group algebras possess quasi-central bounded approximate identities. Reiter-type and structural conditions for such groups are obtained which indicate that these groups behave much like the tractable [SIN]-groups. A general notion of an amenable action on the predual of a von Neumann algebra is developed to prove these theorems. Applications to the cohomology of group and Fourier algebras are discussed.
Citation
Ross Stokke. "Quasi-central bounded approximate identities in group algebras of locally compact groups." Illinois J. Math. 48 (1) 151 - 170, Spring 2004. https://doi.org/10.1215/ijm/1258136179
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