Uniform equicontinuity, multiplier topology and continuity of convolution
We characterise bounded uniformly equicontinuous sets of functions on locally compact groups in terms of uniform factorisation. We apply this result to study the continuity of the convolution product on the dual LUC(G)* of the space of bounded left uniformly continuous functions with the topology of uniform convergence on bounded uniformly equicontinuous sets. When restricted to the space of finite Radon measures on a locally compact group, this is the right multiplier topology. For any topological group, the convolution is jointly continuous on bounded sets in the measure algebra. It is jointly continuous on all of LUC(G)* when G is a locally compact SIN group.
|Keywords||Continuity of convolution, Left uniformly continuous functions, Measure algebra, Topological and locally compact groups, Uniform equicontinuity|
|Journal||Archiv der Mathematik|
Neufang, T, Pachl, J. (Jan), & Salmi, P. (Pekka). (2015). Uniform equicontinuity, multiplier topology and continuity of convolution. Archiv der Mathematik, 104(4), 367–376. doi:10.1007/s00013-015-0726-9