Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance

By Marc Rieffel. 2001

156 citations recorded by the source corpus.

Gromov-Hausdorff distance for quantum metric spaces Bibliography Matrix algebras Converge to the sphere for quantum Gromov-Hausdorff distance Bibliography.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d099b59708462f5c2a8a2a4e59065cf3ecf4e105

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

In Nuclear and High Energy Physics

Citations in the corpus

Matricial quantum Gromov–Hausdorff distance (2002, methodology): “Proposition 1.3 of [ 10 ] then shows that S(A) is in the γ-neighbourhood of S(B) under the metric defined by the Lip-norm L on A ⊕ B associated to N. But the argument there also applies at the matrix level: given ϕ ∈ UCPn(A) we have ϕ ◦ σ ∈ UCPn(B) since σ is u.c.p., and if L(f, T) ≤ 1 then k f − σT”
On Gromov-Hausdorff convergence for operator metric spaces (2004, methodology): “In addition to Rieffel’s analogues of the Gromov completeness and compactness theorems, there have been developed various convergence and continuity results which apply for instance to θ-deformations [14], quantum tori [19, 12], and Berezin quantization [21] (see also [14]).”
Gromov-Hausdorff Distance for Quantum Metric Spaces (2000, unknown): “O A ] 2 0 Fe b”