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Extensions of Pure States and Projections of Norm One

✍ Scribed by R.J. Archbold

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
159 KB
Volume
165
Category
Article
ISSN
0022-1236

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✦ Synopsis

We show that the extension property for pure states of a C*-subalgebra B of a C*-algebra A leads to the existence of a projection of norm one R: A Γ„ B in the case where B is liminal with Hausdorff primitive ideal space. Furthermore, R is given by a ``Dixmier process'' in which the averaging is effected by a group of unitary elements in the centre of the multiplier algebra M(B). These results generalize earlier work of J. Anderson and the author for the case when B is a masa of A. Various applications are given in the context of inductive limit algebras such as AF algebras and, more generally, Kumjian's ultraliminary C*-algebras.

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