Tuesday, March 26, 2019, 17:15

Wrocław University of Technology, 215 D-1

Speaker: Damian Sobota (Universityof Viena)

Title: Josefson-Nissenzweig theorem for $C(K)$-spaces

Abstract:

The Josefson-Nissenzweig theorem is a powerful tool in Banach space theory. Its special version for Banach spaces of continuous functions reads as follows: for a given infinite compact space K there exists a sequence $(\mu_n)$ of normalized signed Radon measures on K such that the integrals $\mu_n(f)$ converge to $0$ for any function $f$ in $C(K)$. During my talk I will investigate when the sequence $(\mu_n)$ can be chosen in such a way that every $\mu_n$ is just a finite linear combination of Dirac point measures (in other words, $\mu_n$ has finite support). This will appear to have connections with the Grothendieck property of Banach spaces and complementability of the space $c_0$. In particular, I’ll present a very elementary proof that $c_0$ is always complemented in a space $C(K\times K)$.