Dixmier traces are weak ⁎ dense in the set of all fully symmetric traces

Spectral Flow and Dixmier Traces

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 Neumann algebra. Our results have several applications. We deduce a formula for the Chern character of an odd L-summable Breuer-Fredholm module in terms of a Hochschild 1-cycle. We explain how to derive a Wodzicki res...

Dixmier traces and coarse multifractal analysis

We show how multifractal properties of a measure supported by a fractal F ⊆ [0, 1] may be expressed in terms of complementary intervals of F and thus in terms of spectral triples and the Dixmier trace of certain operators. For self-similar measures this leads to a non-commutative integral over F equivalent to integration with respect to an auxiliary multifractal measure.

Weak Crossover and the Absence of Traces

We provide a new definition of the linear prominence constraints between pronouns and operators (wh-words and quantifiers) which correctly rules out examples that violate weak crossover. Previous analyses of weak crossover relied on the presence of a trace in the extraction site of a wh-question; in contrast, our analysis enables a traceless account of examples previously cited in support of tr...

All traces lead to ROMA

A note on traces of set families

A family of sets F ⊆ 2[n] is defined to be l-trace k-Sperner if for any l-subset L of [n] the family of traces F|L = {F ∩L : F ∈ F} does not contain any chain of length k+ 1. In this paper we prove that for any positive integers l′, k with l′ < k if F is (n−l′)-trace k-Sperner, then |F| ≤ (k − l′ + o(1)) ( n bn/2c ) and this bound is asymptotically tight. AMS subject classification: 05D05