Equivalence of Quantum Metrics with a common domain
Equivalence of Quantum Metrics with a common domain
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DOI：
10.1016/j.jmaa.2016.05.045
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发表时间：
2016-04
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影响因子：
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通讯作者：
F. Latrémolière
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文献类型：
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作者：
F. Latrémolière
我们刻画了量子紧度量空间之间的Lipschitz态射为那些 *-态射，它们保持Lipschitz范数的某些非交换类似物的域，即下半连续Lip-norms。作为推论，具有共享区域的下半连续Lip-norms实际上是等价的。然后，我们注意到，当一个家庭的下半连续李普-范数是一致等价的，那么他们会产生完全有界类的量子紧度量空间，我们将这一观察到的几个例子扰动的量子度量空间。我们还构造了量子紧度量空间之间Lipschitz距离的非对易推广。
We characterize Lipschitz morphisms between quantum compact metric spaces as those *-morphisms which preserve the domain of certain noncommutative analogues of Lipschitz seminorms, namely lower semi-continuous Lip-norms. As a corollary, lower semi-continuous Lip-norms with a shared domain are in fact equivalent. We then note that when a family of lower semi-continuous Lip-norms are uniformly equivalent, then they give rise to totally bounded classes of quantum compact metric spaces, and we apply this observation to several examples of perturbations of quantum metric spaces. We also construct the noncommutative generalization of the Lipschitz distance between quantum compact metric spaces.