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(H) has a pure state that is not multiplicative on any masa
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Department of Mathematics, University of California, Santa Barbara, CA 93106; and Department of Mathematics, Washington University in Saint Louis, Saint Louis, MO 63130
Edited by Richard V. Kadison, University of Pennsylvania, Philadelphia, PA, and approved February 7, 2008 (received for review February 5, 2008)
Assuming the continuum hypothesis, we prove that 
(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.
bounded operators | Hilbert space
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
To whom correspondence should be addressed. E-mail: akemann{at}math.ucsb.edu
© 2008 by The National Academy of Sciences of the USA
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