59 citations · 221 across the 7 of their papers we have counts for
7 papers
Traces of compact operators and the noncommutative residue
Nigel Kalton, Steven Lord, Denis Potapov +1
We extend the noncommutative residue of M. Wodzicki on compactly supported classical pseudo-differential operators of order and generalise A. Connes' trace theorem, which stat…
Riemannian manifolds in noncommutative geometry
Steven Lord, Adam Rennie, Joseph C. Varilly
We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from nonco…
Measure Theory in Noncommutative Spaces
Steven Lord, Fedor Sukochev
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…
Noncommutative Residues and a Characterisation of the Noncommutative Integral
Steven Lord, Fedor A. Sukochev
We continue the study of the relationship between Dixmier traces and noncommutative residues initiated by A. Connes. The utility of the residue approach to Dixmier traces is shown…
Measures from Dixmier Traces and Zeta Functions
Steven Lord, Denis Potapov, Fedor Sukochev
For essentially bounded functions on a (closed) compact Riemannian manifold, the noncommutative residue and the Dixmier trace formulation of the noncommutative integral are shown t…
Dixmier Traces as Singular Symmetric Functionals and Applications to Measurable Operators
Steven Lord, Aleksandr Sedaev, Fyodor Sukochev
This paper introduces a new approach to the non-normal Dixmier and Connes-Dixmier traces (introduced by Dixmier and adapted to non-commutative geometry by Connes) on a general Marc…