Approximation Of C～*-algebras With An Ergodic Action Of Group By Finite Dimensional Quantized Metric Spaces

By a quantized metric space, we mean a pair (A, (?)) consisting of a matrix order unit space (A, 1) with a matrix Lip-norm (?) defined on it. Gromov-Hausdorff distance on quantized metric spaces generalizes Gromov-Hausdorff distance on metric spaces to non-commutative spaces, we prove that for a quantized metric space (A,(?)), a compact group G and an action α of G on A, there exists a sequence of finite-dimensional quantized metric spaces (B_n, (?)|s_n) such that (A, C) is the limit of {(B_n, (?)|B_n)} with respect to quantized Gromov-Hausdorff distance.