### 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

### Cite this

**Extensions of pure states and projections of norm one II.** / Archbold, Robert J.

Research output: Contribution to journal › Article

*Bulletin of the London Mathematical Society*, vol. 33, pp. 67-72.

}

TY - JOUR

T1 - Extensions of pure states and projections of norm one II

AU - Archbold, Robert J

PY - 2001

Y1 - 2001

N2 - 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).

AB - 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).

KW - C-STAR-ALGEBRAS

KW - OPERATOR-ALGEBRAS

KW - REPRESENTATIONS

M3 - Article

VL - 33

SP - 67

EP - 72

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

ER -