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Note on the Kasparov Product of C*-algebra Extensions
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- Journal:
- Canadian Mathematical Bulletin / Volume 56 / Issue 4 / 01 December 2013
- Published online by Cambridge University Press:
- 20 November 2018, pp. 870-880
- Print publication:
- 01 December 2013
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- Article
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Using the Dadarlat isomorphism, we give a characterization for the Kasparov product of
${{C}^{*}}$-algebra extensions. A certain relation between 
$KK\left( A,\,Q\left( B \right) \right)$ and 
$KK\left( A,\,Q\left( KB \right) \right)$ is also considered when 
$B$ is not stable, and it is proved that $KK\left( A,\,Q\left( B \right) \right)$ and $KK\left( A,\,Q\left( KB \right) \right)$ are not isomorphic in general.
