The problem of completeness for Gromov-Hausdorff metrics on C*-algebras

摘要

M. Rieffel, up to complete order isomorphisms preserving the Lip-seminorm, is not complete w.r.t. the matricial quantum Gromov-Hausdorff distance introduced by D. Kerr. This is shown by exhibiting a Cauchy sequence whose limit, which always exists as an operator system, is not completely order isomorphic to any C*-algebra.