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Marc A. Rieffel

机译：马克·A·里弗尔

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In contrast to the usual Lipschitz seminorms associated to ordinarymetrics on compact spaces, we show by examples that Lipschitz seminorms onpossibly non-commutative compact spaces are usually not determined by therestriction of the metric they define on the state space, to the extremepoints of the state space. We characterize the Lipschitz norms which aredetermined by their metric on the whole state space as being those which arelower semicontinuous. We show that their domain of Lipschitz elements can beenlarged so as to form a dual Banach space, which generalizes the situationfor ordinary Lipschitz seminorms. We give a characterization of the metricson state spaces which come from Lipschitz seminorms. The natural (broader)setting for these results is provided by the ``function spaces'' of Kadison.A variety of methods for constructing Lipschitz seminorms is indicated.
机译：与紧凑空间上与范式相关的通常的Lipschitz半范数相反，我们通过示例表明，可能非交换紧凑空间的Lipschitz半范数通常不是由它们在状态空间上定义的度量约束到状态空间的极点来确定的。 。我们将由其在整个状态空间上的度量所确定的Lipschitz规范表征为较低半连续的规范。我们表明，可以扩大Lipschitz元素的域，以形成对偶Banach空间，从而推广了普通Lipschitz半范数的情况。我们给出了来自Lipschitz半范数的度量状态空间的表征。这些结果的自然（更广泛）设置是由Kadison的``函数空间''提供的，并指出了多种构建Lipschitz半范数的方法。

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