Gromov-Hausdorff distance for quantum metric spaces ; matrix algebras converge to the sphere for quantum Gromov-Hausdorff distance
著者
書誌事項
Gromov-Hausdorff distance for quantum metric spaces ; matrix algebras converge to the sphere for quantum Gromov-Hausdorff distance
（Memoirs of the American Mathematical Society, no. 796）
American Mathematical Society, 2004
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注記
"March 2004, volume 168, number 796 (first of 4 numbers)."
Includes bibliographical references (p. 63-65, p. 89-91)
内容説明・目次
内容説明
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 $A_\theta$.
目次
Gromov-Hausdorff distance for quantum metric spaces Bibliography Matrix algebras Converge to the sphere for quantum Gromov-Hausdorff distance Bibliography.
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