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