Operator systems and extensions of positive semi-definite functionsOberseminar Global Analysis and Operator Algebras

by Malte Leimbach (MPIM Bonn)

Tuesday Jun 2, 2026, 2:15 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60/1-008 (Mathezentrum)

The extension problem is a classical problem from harmonic
analysis, and asks whether positive semi-definite functions on a
symmetric unital subset of a discrete group can be extended to positive
semi-definite functions on the whole group. It has been known at least
since the work of Rudin in the 1960s that this is closely related to the
problem of finding sums of squares factorisations of positive elements
in the group C*-algebra. In this talk I will give an operator system
perspective at these two problems, explaining their equivalence, and how
they are linked to the question about duality of the operator systems
which have recently emerged from spectral and Fourier truncations in
noncommutative geometry. I will also provide some background on the
required operator system techniques, and give discuss some examples from
our point of view. Based on arXiv:2603.29958, joint with Evgenios
Kakariadis, Ivan Todorov, and Walter van Suijlekom.