This book is the first complete study and monograph dedicated to singular traces. The text
mathematically formalises the study of traces in a self contained theory of functional …

A Banach limit is a positive shift-invariant functional on ℓ∞ which extends the functional (x1,
x2,...)↦→ lim n→∞ xn from the set of convergent sequences to ℓ∞. The history of Banach …

This is a discussion of recent progress in the theory of singular traces on ideals of compact
operators, with emphasis on Dixmier traces and their applications in non-commutative …

We obtain general theorems which enable the calculation of the Dixmier trace in terms of the
asymptotics of the zeta function and of the heat operator in a general semi-finite von …

We introduce a new approach to traces on the principal ideal L 1,∞ generated by any
positive compact operator whose singular value sequence is the harmonic sequence …

We generalise the local index formula of Connes and Moscovici to the case of spectral
triples for a*-subalgebra A of a general semifinite von Neumann algebra. In this setting it …

Let ℓ∞ be the space of all bounded sequences x=(x1, x2,…) with the norm and let L (ℓ∞) be
the set of all bounded linear operators on ℓ∞. We present a set of easily verifiable sufficient …

Given a spectral triple (A, H, D), the functionals on A of the form a↦ τω (a| D|− α) are studied,
where τω is a singular trace, and ω is a generalised limit. When τω is the Dixmier trace, the …

We obtain general theorems which enable the calculation of the Dixmier trace in terms of the
asymptotics of the zeta function and of the trace of the heat semigroup. We prove our results …

The analytic approach to spectral flow is about ten years old. In that time it has evolved to
cover an ever wider range of examples. The most critical extension was to replace Fredholm …