Advances in Dixmier traces and applications

A direct approach to positive normalised traces on simply generated ideals

“…Moreover, we prove that the cardinality of the set of such traces is 2 2 N 0 . This answers a question raised in a recent survey [11].…”

Quantum Differentiability on Quantum Tori

“…A trace ϕ is called continuous if it is continuous with respect to the L 1,∞ quasi-norm. It is known that not all traces on L 1,∞ are continuous [38,Remark 3.1(3)]. Within the class of continuous traces on L 1,∞ there are the well-known Dixmier traces [37,Chapter 6].…”

Connes Integration Formula without singular traces

“…In fact, ϕ vanishes on the ideal L 1 (see [10] or [21]). For the state of the art in the theory of singular traces and their applications in Non-commutative Geometry, we refer the reader to the survey [22].…”