Geodesic
A Counterexample in the Perturbation Theory of C*-Algebras
Canadian mathematical bulletin, Tome 25 (1982) no. 3, pp. 311-316

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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.
DOI : 10.4153/CMB-1982-043-4
Mots-clés : 46L05 
Johnson, B. E. A Counterexample in the Perturbation Theory of C*-Algebras. Canadian mathematical bulletin, Tome 25 (1982) no. 3, pp. 311-316. doi: 10.4153/CMB-1982-043-4
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[1] 1. Christensen, E., Perturbation of operator algebras, Invent. Math. 43 (1977), 1-13. Google Scholar

[2] 2. Christensen, E., Near inclusions of C*-algebras, Copenhagen preprint series no. 5, 1978. Google Scholar

[3] 3. Dixmier, J., Les algèbres d'opérateurs dans l'espace hilbertien (Algèbres de von Neumann), Gauthier-Villars, Paris 1969. Google Scholar

[4] 4. Halmos, P. R., A Hilbert space problem book, Van Nostrand, New Jersey 1967. Google Scholar

[5] 5. Johnson, B. E., Perturbations of Banach algebras, Proc. London Math. Soc. 34 (1977), 439-458. Google Scholar

[6] 6. Kelley, J. L., General Topology, Van Nostrand, Princeton 1955. Google Scholar

[7] 7. Phillips, J. and Raeburn, I., Perturbation of operator algebras, II, Proc. London Math. Soc. 43 (1981), 46-72. Google Scholar

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