Almost every mathematician working in von Neumann algebras says that there are certainly extremely disconnected compact spaces $K$ such that $C(K)$ is not a dual space (they are not hyperstonean). Everyone points out the following reference:
J. Dixmier, Sur certains espaces consideres par M. H. Stone, Summa Bras. Math. 2 (1951), 151–182.
Unfortunately, my French does not exist but this not a real obstacle. The problem is that this article seems to be unavailable. Can one describe me please how does this counter-example look like? Are there any other known such counter-examples?
I am aware that there are certain topological characterisations of hyperstonean spaces by several Russian mathematicians but they are not easy to verify. This is why I am just interested in concrete spaces rather than general theorems.