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Gromov-Hausdorff distance for quantum metric spaces : matrix algebras converge to the sphere for quantum Gromov-Hausdorff distance by Marc Aristide Rieffel is a nonfiction available to read on EtoBox.

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<p>By a quantum metric space we mean a $C^*$-algebra (or more generally an order-unit space) equipped with a generalization of the usual Lipschitz seminorm on functions which one associates to an ordinary metric. We develop for compact quantum metric spaces a version of Gromov-Hausdorff distance. We show that the basic theorems of the classical theory have natural quantum analogues. Our main example involves the quantum tori, $A_\theta$. We show, for consistently defined ''metrics'', that if a sequence $\{\theta_n\}$ of parameters converges to a parameter $\theta$, then the sequence $\{A_{\theta_n}\}$ of quantum tori converges in quantum Gromov-Hausdorff distance to $A_\theta$.</p>

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Author

Marc Aristide Rieffel

Publisher

American Mathematical Society

Published

2004

Language

EN

ISBN

9780821834954

Category

nonfiction

Subjects

Mathematics, Science, Physics