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Purely infinite C*-algebras of real rank zero

✍ Scribed by Pasnicu, Cornel; Rørdam, Mikael

Book ID
118741231
Publisher
Walter de Gruyter GmbH & Co. KG
Year
2007
Tongue
English
Weight
219 KB
Volume
2007
Category
Article
ISSN
0075-4102

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✦ Synopsis

We show that a separable purely infinite C Ã -algebra is of real rank zero if and only if its primitive ideal space has a basis consisting of compact-open sets and the natural map K 0 ðI Þ ! K 0 ðI =JÞ is surjective for all closed two-sided ideals J H I in the C Ãalgebra. It follows in particular that if A is any separable C Ã -algebra, then A n O 2 is of real rank zero if and only if the primitive ideal space of A has a basis of compact-open sets, which again happens if and only if A n O 2 has the ideal property, also known as property (IP).

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