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A Counterexample in the Perturbation Theory of C*-Algebras

Published online by Cambridge University Press:  20 November 2018

B. E. Johnson
B. E. Johnson*
Affiliation:
The University Newcastle Upon Tyne, England
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Abstract

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The strongest positive results in the stability theory of C*-algebras assert that if are sufficiently close C*-subalgebras of (H) of certain kinds, then there is a unitary operator U on H near I, such that . We give examples of C*-algebras , both isomorphic to the algebra of continuous functions from [0, 1] to the algebra of compact operators on Hilbert space, which can be as close as we like, yet for which there is no isomorphism α: → with . Thus the results mentioned do not extend to these C*-algebras.

Keywords

46L05

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 3 , 01 September 1982 , pp. 311 - 316
Copyright
Copyright © Canadian Mathematical Society 1982

References

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