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| SPLIT INCLUSION AND METRICALLY NUCLEAR MAP |
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Citation： |
Wu Liangsen.SPLIT INCLUSION AND METRICALLY NUCLEAR MAP[J].Chinese Annals of Mathematics B,1997,18(1):113~118 |
| Page view： 1025
Net amount： 776 |
Authors： |
Wu Liangsen; |
Foundation： |
Project supported by the National Natural Science
Foundation of China |
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| Abstract： |
The author relates the split inclusion property to the metrically nuclearty
of the natural embedding $\phi_1$ and proves the following result.
Let $A\subset B$ be an inclusion of factors, $\omega$
a faithful normal state of $B$ such that $\omega=(\cdot \Omega,\Omega)$. If
$\phi_1: A\to L^1(B)$ defined by $\phi_1(x)=(\cdot \Omega,J_Bx\Omega), \forall x\in
A,$ is the natural embedding, then $(A,B)$ is a split inclusion if and only
if $\phi_1$ is a metrically nuclear map. |
Keywords： |
Von Neumann algebra, Split inclusion, Metrically nuclear map |
Classification： |
54C25 |
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