Steven Lord, Fedor Sukochev, “Measure Theory in Noncommutative Spaces”, SIGMA, 2010, Volume 6,072, 36 pp.

This article is cited in 8 papers

Measure Theory in Noncommutative Spaces

Steven Lord^a, Fedor Sukochev^b

^a School of Mathematical Sciences, University of Adelaide, Adelaide, 5005, Australia
^b University of New South Wales, School of Mathematics and Statistics

Abstract: The integral in noncommutative geometry (NCG) involves a non-standard trace called a Dixmier trace. The geometric origins of this integral are well known. From a measure-theoretic view, however, the formulation contains several difficulties. We review results concerning the technical features of the integral in NCG and some outstanding problems in this area. The review is aimed for the general user of NCG.

Keywords: Dixmier trace; singular trace; noncommutative integration; noncommutative geometry; Lebesgue integral; noncommutative residue.

MSC: 46L51; 47B10; 58B34

Received: March 25, 2010; in final form August 4, 2010; Published online September 16, 2010

Language: English

DOI: 10.3842/SIGMA.2010.072