Geometric aspects of similarity problems

Date

Jun 21, 2017

Time

5:00 PM - 6:00 PM

Speaker

Martín Miglioli

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Dr. Vadim Alekseev

Description

Some similarity problems study conditions under which a unital homomorphism between operator algebras is conjugated to a self-adjoint homomorphism. We study aspects of these problems through the isometric action of the invertible elements of a C*-algebra on the positive invertible elements given by g.a=gag*. Minimality properties of projections to closed convex sets in the non-positively curved cone of positive invertible operators are used to study minimality properties of canonical orthogonalizers of some unital algebra homomorphisms. The convexity of the distance along geodesics is used to prove interpolation results of norms of conjugated representations. We also address the question of existence of unitarizers of groups of invertible operators when these groups act on manifolds of positive invertible operators endowed with a metric derived from a trace. Here the Bruhat–Tits fixed point theorem is used to show that the square root of the circumcenter of orbits are unitarizers of the groups.

Links

• Seminar Geometrie

Last modified: Jun 19, 2017, 11:28:15 AM