Abstract
It is shown that the class of amenable (resp. strongly amenable)C*-algebras is closed under the process of taking crossed products with discrete amenable groups. Under certain circumstances, amenability is also preserved under taking a “crossed product” with an amenable semigroup of linear endomorphisms. These facts are used to show that certain simpleC*-algebras\(\mathcal{O}_n \) studied by J. Cuntz are amenable but not strongly amenable (thus answering a question of B. E. Johnson), yet are stably isomorphic to strongly amenable algebras.
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Brown, L.G., Green, P., Rieffel, M.A.: Stable isomorphism and strong Morita equivalence ofC*-algebras. Pacific J. Math.71, 349–364 (1977)
Bunce, J.: Characterizations of amenable and strongly amenableC*-algebras. Pacific J. Math.43, 563–572 (1972)
Connes, A.: On the cohomology of operator algebras. Preprint
Cuntz, J.: SimpleC*-algebras generated by isometries. Commun. math. Phys.57, 173–185 (1977)
Dixmier, J.: Traces sur lesC*-algèbres II. Bull. Sci. Math.88, 39–57 (1964)
Glimm, J.G.: On a certain class of operator algebras. Trans. Am. Math. Soc.95, 318–340 (1960)
Johnson, B.E.: Cohomology in Banach algebras. Mem. Am. Math. Soc.127 (1972)
Ringrose, J.: Automatic continuity of derivations of operator algebras. J. London Math. Soc.5, 432–438 (1972)
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Communicated by H. Araki
Partially supported by NSF
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Rosenberg, J. Amenability of crossed products ofC*-algebras. Commun.Math. Phys. 57, 187–191 (1977). https://doi.org/10.1007/BF01625777
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DOI: https://doi.org/10.1007/BF01625777