B(H) has a pure state that is not multiplicative on any masa.
Assuming the continuum hypothesis, we prove that Bernoulli function(H) has a pure state whose restriction to any masa is not pure. This resolves negatively old conjectures of Kadison and Singer and of Anderson.
Akemann
Charles
C
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA. akemann@math.ucsb.edu
Weaver
Nik
N