Appears in collection : Operator Algebras and Quantum Information Theory

On the (p,1) Lorentz scale of normed ideals of compact operators, the Macaev ideal is the end at infinity. From a perturbation point of view the Macaev ideal is related to entropy, while finite p is related to Hausdorff dimension p . For discrete groups, connections to supramenability have appeared, via the regular representation. Also properties of commutants mod the Macaev ideal and of associated exotic coronas will be discussed. Dan Voiculescu (UC Berkeley)