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EXTENSIONS OF PURE STATES AND PROJECTIONS OF NORM ONE II

Published online by Cambridge University Press:  18 April 2001

R. J. ARCHBOLD
R. J. ARCHBOLD
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, King's College, Aberdeen AB24 3UE; e-mail: [email protected]
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Abstract

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 Bˆ → 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).

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 1 , January 2001 , pp. 67 - 72
Copyright
© The London Mathematical Society 2001

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