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Tensor Products of C*-Algebras with the Ideal Property

✍ Scribed by Cornel Pasnicu; Mikael Rørdam

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
126 KB
Volume
177
Category
Article
ISSN
0022-1236

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✦ Synopsis

Combining a construction of Dadarlat of a unital, simple, non-exact C*-algebra C of real rank zero and stable rank one, which is shape equivalent to a UHFalgebra, with results of Kirchberg and a result obtained by Dadarlat and the firstnamed author, we show that B(H) C contains an ideal that is not generated by its projections. We also find a unital, separable sub C*-algebra A of B(H) such that A is of real rank zero and A C has an ideal that is not generated by its projections.

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