| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 1898421 | Journal of Geometry and Physics | 2016 | 21 Pages |
Abstract
In the present paper we review recent advances in the theory of Dixmier traces and aspects of their application to noncommutative analysis and geometry. We describe J. Dixmier’s original construction of singular traces together with recent revisions of his ideas. We pay particular attention to subclasses of Dixmier traces related to exponentiation invariant extended limits and notions of measurability due to A. Connes. We discuss in detail the applications of Dixmier traces to the study of spectral properties of pseudo-differential operators and a very recent application of Dixmier traces in the study the Fréchet differentiability of Haagerup’s LpLp norm.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Fedor Sukochev, Alexandr Usachev,