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EXTENSIONS OF PURE STATES AND PROJECTIONS OF NORM ONE II
Published online by Cambridge University Press: 18 April 2001
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).
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- © The London Mathematical Society 2001
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