2006/01/02 by Erik Christensen, Christensen, Erik, Cristina Ivan +1
Mathematics · #46L85 #58B34 #Advanced Operator Algebra Research #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Operator Algebras (math.OA) #math.MG #math.OA #msc:46L85 #msc:58B34
paper · pdf · doi:10.48550/arxiv.math/0601024
27 pages
arxiv created 2006/01/02 · openalex publication_date 2006/01/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study countable sums of two dimensional modules for the continuous complex functions on a compact metric space and show that it is possible to construct a spectral triple which gives the original metric back. This spectral triple will be finitely summable for any positive parameter. We also construct a sum of two dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. We make an explicit computation of the last module for the unit interval. The metric is recovered exactly, the Dixmier trace induces a multiple of the Lebesgue integral and the number N(K) of eigenvalues bounded by K behaves, such that N(K)/K is bounded, but without limit for K growing.