Speaker
Malte Leimbach, Max-Planck-Institut für Mathematik
Abstract
An old problem in harmonic analysis asks whether positive semi-definite functions on a given symmetric unital subset of a discrete group admit extensions to the whole group. We rephrase this question in terms of operator systems by using its relation to the problem of finding sums of squares factorizations of positive elements in the group C*-algebra. Our operator system perspective allows for using knowledge about the extension problem to infer properties of certain associated operator systems and vice versa. We exemplify this by giving a new proof that failure of (min,max)-nuclearity of the operator system of $n \times n$ Toeplitz matrices is witnessed by itself. Moreover, we use the C*-envelope to show that a certain symmetric unital subset of $\mathbb{Z}^2$ does not have the extension property. This talk is based on joint work with Evgenios Kakariadis, Ivan Todorov, and Walter van Suijlekom.