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Extensions of Pure States and Projections of Norm One II
Author(s) -
Archbold R. J.
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/33.1.67
Subject(s) - mathematics , injective function , unitary state , norm (philosophy) , pure mathematics , multiplier (economics) , algebra over a field , political science , law , economics , macroeconomics
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^ → 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 ).