2009/12/15 by A. Carey, Alan L. Carey, Carey, A. +9
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA
paper · pdf · doi:10.48550/arxiv.0912.2817
36 pages
arxiv created 2009/12/15 · openalex publication_date 2009/12/15 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an ab initio approach to integration theory for nonunital spectral triples. This is done without reference to local units and in the full generality of semifinite noncommutative geometry. The main result is an equality between the Dixmier trace and generalised residue of the zeta function and heat kernel of suitable operators. We also examine definitions for integrable bounded elements of a spectral triple based on zeta function, heat kernel and Dixmier trace techniques. We show that zeta functions and heat kernels yield equivalent notions of integrability, which imply Dixmier traceability.