Geometric aspects of similarity problems

Datum

21.06.2017

Zeit

17:00 - 18:00

Sprecher

Martín Miglioli

Sprache

en

Hauptthema

Mathematik

Andere Themen

Mathematik

Host

Dr. Vadim Alekseev

Beschreibung

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

Letztmalig verändert: 19.06.2017, 11:28:15