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| WHEN CAN THE STABLE ALGEBRA DETERMINE THE STRUCTURE OF A C*-ALGEBRA |
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Citation： |
Wu Liangsen.WHEN CAN THE STABLE ALGEBRA DETERMINE THE STRUCTURE OF A C*-ALGEBRA[J].Chinese Annals of Mathematics B,1994,15(2):153~156 |
| Page view： 877
Net amount： 757 |
Authors： |
Wu Liangsen; |
Foundation： |
Project supported by the National Natural Science Foundation of China |
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| Abstract： |
Let $A$ and $B$ be $C^*$-algebras. Suppose that ${\Cal K}$ is the algebra of all
compact operators on a seperable Hilbert space, and $\alpha$ is an action
on the stable algebra ${\Cal K}\otimes A$ induced by $SU(\infty)$.
It is proved that if $A$ is $\alpha$-invariant stable isomorphic to $B$,
then there is a *-isomorphism between $A$ and $B$.
An analogous result is obtained by
considering $O_n\otimes{\Cal K}\otimes A$ in the place of ${\Cal K}
\otimes A$, where $O_n$ is the Cuntz algebra $(3\le n <\infty)$. |
Keywords： |
$C^*$-algebra, Stable algebra, Cuntz algebra, $\al$-invariance. |
Classification： |
46L05 |
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