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| TOEPLITZ ALGEBRAS ON DISCRETE GROUPSAND THEIR NATURAL MORPHISMS |
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Citation： |
J. LORCH,XU Qingxiang.TOEPLITZ ALGEBRAS ON DISCRETE GROUPSAND THEIR NATURAL MORPHISMS[J].Chinese Annals of Mathematics B,2005,26(1):143~152 |
| Page view： 1162
Net amount： 863 |
Authors： |
J. LORCH; XU Qingxiang |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10371051). |
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| Abstract： |
Let $G$ be a discrete group, $E_1$ and $E_2$ be two subsets of $G$
with $E_1\subseteq E_2$, and $e\in E_2$. Denote by ${\cal
T}^{E_1}$ and ${\cal T}^{E_2}$ the associated Toeplitz algebras.
In this paper, it is proved that the natural morphism
$\gamma^{E_2,E_1}$ from ${\cal T}^{E_1}$ to ${\cal T}^{E_2}$
exists as a $C^*$-morphism if and only if $E_2$ is finitely
covariant-lifted by $E_1$. Based on this necessary and sufficient
condition, some applications are made. |
Keywords： |
Toeplitz
algebra, Natural $C^*$-morphism, Finite covariant-lift |
Classification： |
47B35 |
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