Probabilistic Operator Algebra Seminar: The Macaev norm, entropy and supramenability

Seminar | September 25 | 3:45-5:45 p.m. | 748 Evans Hall

 Dan-Virgil Voiculescu, UC Berkeley

 Department of Mathematics

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 (Kolmogorov-Sinai dynamical entropy and Avez entropy of random walks on groups), 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.