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Bulletin of the London Mathematical Society 2001 33(1):67-72; doi:10.1112/blms/33.1.67
© 2001 by London Mathematical Society
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© London Mathematical Society

Extensions of Pure States and Projections of Norm One II

R. J. Archbold

Department of Mathematical Sciences, University of Aberdeen, King's College Aberdeen AB24 3UE; e-mail: r.archbold{at}maths.abdn.ac.uk

Received 5 November 1999. Revision received 29 February 2000.

It is shown that if a C*-algebra A contains a semi-scattered C*-algebra B such that the pure states of B and the zero functional extend uniquely to A, and the canonical mapping B^ -> Â is injective, then there exists a (unique) projection of norm one R: A -> B. In certain circumstances, the conditional expectation R can be effected by a unitary averaging process using unitary elements in the centre of the multiplier algebra M(B).


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