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| THE TRACE SPACE INVARIANT AND UNITARY GROUP OF $C^*$-ALGEBRA |
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Citation： |
FANG Xiaochun.THE TRACE SPACE INVARIANT AND UNITARY GROUP OF $C^*$-ALGEBRA[J].Chinese Annals of Mathematics B,2003,24(1):115~122 |
| Page view： 1112
Net amount： 710 |
Authors： |
FANG Xiaochun; |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10271090). |
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| Abstract： |
Let $A$ be a unital $C^*$-algebra, $n\in{\bold N}\cup\{\infty\}$. It is proved
that the isomorphism $\Delta_n:$
$U_0^n(A)/\overline{DU_0^n(A)}\mapsto AffT(A)/\overline{\Delta_n^0(\pi_1
(U_0^n(A)))}$ is isometric for some suitable distances. As an application,
the author has the split exact sequence
$0\mapsto AffT(A)/\overline {\Delta_n^0(\pi_1
(U_0^n(A)))} \overset{i_A}\to{\mapsto}U^n(A)/\overline{DU^n(A)}
\overset{\pi_A}\to{\mapsto} U^n(A)/U^n_0(A)
\mapsto 0
$
with $i_A$ contractive (and isometric if $n=\infty$)
under certain condition of $A$. |
Keywords： |
Trace space, Unitary group, $C^*$-algebra |
Classification： |
46L35, 19K14 |
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