Professor Jan Harm van der Walt from the University of Pretoria has just delivered his lecture at the RGOSA seminar series, titled “Category measures, the dual of and hyper-Stonean spaces”.
The abstract of the talk is here:
For a compact Hausdorff space , we give descriptions of the dual of , the Dedekind completion of the Banach lattice of continuous, real-valued functions on . We characterize those functionals which are -order continuous and order continuous, respectively, in terms of Oxtoby’s category measures. As applications, we give a purely topological characterization of hyper-Stonean spaces, and characterize those spaces for which admits a strictly positive order continuous functional.
Please find the seminar video attached, and the presentation slides below.