### 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 (B) over cap --> (A) over cap 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).

Original language | English |
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Pages (from-to) | 67-72 |

Number of pages | 5 |

Journal | Bulletin of the London Mathematical Society |

Volume | 33 |

Publication status | Published - 2001 |

### Keywords

- C-STAR-ALGEBRAS
- OPERATOR-ALGEBRAS
- REPRESENTATIONS