J. Dixmier published in 1966 a short note devoted to the construction of a “non normal trace”, i.e. a linear form on L(H) (set of all bounded operators in a Hilbert space H), possessing all the algebraic properties of the standard trace, but lacking of some continuity property. We expose in details the construction of the trace, as well as the functional analysis tools used by Dixmier, then the utilization of the Dixmier trace by A. Connes in his Non Commutative Geometry, and also some generalizations to certain von Neumann algebras, other than L(H).
Cite this article
Alain Guichardet, La trace de Dixmier et autres traces. Enseign. Math. 61 (2015), no. 3/4, pp. 461–481DOI 10.4171/LEM/61-3/4-8