Nonuniqueness of the cardinality attached to homogeneous 𝐴𝑊*-algebras
Masanao Ozawa · Proceedings of the American Mathematical Society · 1985
It is proved that for any pair of infinite cardinal numbers α \alpha and β \beta , there exists a homogeneous AW*-algebra that is both α \alpha -homogenous and β \beta -homogeneous. This negatively settles a long-standing unsolved problem of type I AW*-algebras.