On the $K$-groups of certain $C^ *$-algebras used in $E$-theory
HTML articles powered by AMS MathViewer
- by Gabriel Nagy
- Proc. Amer. Math. Soc. 122 (1994), 1125-1131
- DOI: https://doi.org/10.1090/S0002-9939-1994-1209099-3
- PDF | Request permission
Abstract:
Let A be a ${{\text {C}}^ \ast }$-algebra. We denote by ${A_\infty }$ the quotient of the ${{\text {C}}^ \ast }$-algebra of bounded continuous functions $[1,\infty ) \to A$ by the ideal of the functions which vanish at $\infty$. We show that the the canonical map $A \to {A_\infty }$ gives an isomorphism between K-groups, provided that A is stable.References
- Bruce Blackadar, $K$-theory for operator algebras, Mathematical Sciences Research Institute Publications, vol. 5, Springer-Verlag, New York, 1986. MR 859867, DOI 10.1007/978-1-4613-9572-0
- Alain Connes and Nigel Higson, Déformations, morphismes asymptotiques et $K$-théorie bivariante, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), no. 2, 101–106 (French, with English summary). MR 1065438 E. Effros and J. Kaminker, Homotopy continuity and shape theory for ${C^ \ast }$-algebras, Geometric Methods in Operator Algebras, U. S.-Japan Joint Seminar at Kyoto, Pitman, 1983.
- J. A. Mingo, $K$-theory and multipliers of stable $C^\ast$-algebras, Trans. Amer. Math. Soc. 299 (1987), no. 1, 397–411. MR 869419, DOI 10.1090/S0002-9947-1987-0869419-7
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 1125-1131
- MSC: Primary 46L80; Secondary 19K56
- DOI: https://doi.org/10.1090/S0002-9939-1994-1209099-3
- MathSciNet review: 1209099