Gromov-Hausdorff distance for quantum metric spaces
نویسندگان
چکیده
منابع مشابه
Gromov–hausdorff Distance for Quantum Metric Spaces
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 ...
متن کاملMatricial Quantum Gromov-hausdorff Distance
We develop a matricial version of Rieffel’s Gromov-Hausdorff distance for compact quantum metric spaces within the setting of operator systems and unital C∗-algebras. Our approach yields a metric space of “isometric” unital complete order isomorphism classes of metrized operator systems which in many cases exhibits the same convergence properties as those in the quantum metric setting, as for e...
متن کاملC∗-algebraic Quantum Gromov-hausdorff Distance
We introduce a new quantum Gromov-Hausdorff distance between C∗-algebraic compact quantum metric spaces. Because it is able to distinguish algebraic structures, this new distance fixes a weakness of Rieffel’s quantum distance. We show that this new quantum distance has properties analogous to the basic properties of the classical Gromov-Hausdorff distance, and we give criteria for when a parame...
متن کاملOrder-unit Quantum Gromov-hausdorff Distance
We introduce a new distance distoq between compact quantum metric spaces. We show that distoq is Lipschitz equivalent to Rieffel’s distance distq, and give criteria for when a parameterized family of compact quantum metric spaces is continuous with respect to distoq. As applications, we show that the continuity of a parameterized family of quantum metric spaces induced by ergodic actions of a f...
متن کاملComputing the Gromov-Hausdorff Distance for Metric Trees
The Gromov-Hausdorff distance is a natural way to measure distance between two metric spaces. We give the first proof of hardness and first non-trivial approximation algorithm for computing the Gromov-Hausdorff distance for geodesic metrics in trees. Specifically, we prove it is NP-hard to approximate the Gromov-Hausdorff distance better than a factor of 3. We complement this result by providin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Memoirs of the American Mathematical Society
سال: 2004
ISSN: 0065-9266,1947-6221
DOI: 10.1090/memo/0796