𝐾-theory and multipliers of stable 𝐶*-algebras

Mingo, J. A.

doi:10.1090/S0002-9947-1987-0869419-7

$K$-theory and multipliers of stable $C^ \ast$-algebras
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by J. A. Mingo

Trans. Amer. Math. Soc. 299 (1987), 397-411

DOI: https://doi.org/10.1090/S0002-9947-1987-0869419-7

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Abstract:

The main theorem is that if $A$ is a $C^{\ast }$-algebra with a countable approximate identity consisting of projections, then the unitary group of $M(A \otimes K)$ is contractible. This gives a realization, via the index map, of ${K_0}(A)$ as components in the set of Fredholm operators on ${H_A}$.

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