AG Mathematisch Physik, Malte Leimbach (Bonn): Compact quantum metric spaces and spectral truncations

Malte Leimbach (Bonn)

Compact quantum metric spaces and spectral truncations

Abstract:
Starting from Connes‘ distance formula, Rieffel generalized Lipschitz
constants of functions to so-called Lip-norms of bounded operators.
Lip-norms induce metrics on state spaces and a crucial requirement is
that these metrics induce the weak* topology, in which case one speaks
of a compact quantum metric space. There are various quantum versions of
Gromov–Hausdorff distance allowing for considering questions about
convergence of compact quantum metric spaces. In this talk I will focus
on compact quantum metric spaces modeled on operator systems and
Kerr–Li’s operator Gromov–Hausdorff distance. I will discuss some
convergence results related to the spectral truncations put forward by
Connes–van Suijlekom.