Extensions of pure states and projections of norm one II

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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 (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 languageEnglish
Pages (from-to)67-72
Number of pages5
JournalBulletin of the London Mathematical Society
Volume33
Publication statusPublished - 2001

Keywords

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

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