C*-unique groupoids

Eduard Ortega (Norwegian University of Science and Technology)

Thursday 26th March, 2020 15:00-16:00 Zoom


The notion of C*-unique Banach *-algebras was introduced in the 80's by Boidol, meaning that a Banach *-algebra accepts just one C*-norm. This concept was then specialize to the case of the Banach group algebras L^1(G), saying that a group is  C*-unique if L^1(G) is C*-unique. An obvious necessary condition is amenability of the group, but turns out not to be sufficient, at least in the locally compact case.  Applications of C*-uniqueness can be found in measure theory, in the so-called Pompeiu Problem, but also in Gabor analysis, since it was proved  by Gröchening and Leinert that C*-uniqueness together with symmetry of the Banach algebra implies spectral invariance. In this talk I will talk about C*-uniqueness of the Banach *-algebra L^1(G) for an étale groupoid G, and give conditions for when it is C*-unique. Unless, the group case (topological) amenability it is no longer a necessary condition, but instead the weak containment property. This is a joint work with Are Austad.

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