Proof of the Ghahramani-Lau conjecture
The Ghahramani-Lau conjecture is established; in other words, the measure algebra of every locally compact group is strongly Arens irregular. To this end, we introduce and study certain new classes of measures (called approximately invariant, respectively, strongly singular) which are of interest in their own right. Moreover, we show that the same result holds for the measure algebra of any (not necessarily locally compact) Polish group.
|Keywords||Arens product, Locally compact group, Measure algebra, Separation of measures, Thin measure, Topological centre|
|Journal||Advances in Mathematics|
Losert, V. (Viktor), Neufang, T, Pachl, J. (Jan), & Steprans, J. (Juris). (2016). Proof of the Ghahramani-Lau conjecture. Advances in Mathematics, 290, 709–738. doi:10.1016/j.aim.2015.12.004