Damian Sobota: Josefson-Nissenzweig theorem for C(K)-spaces
23/03/19 04:04
Tuesday, March 26, 2019 17:15
Room: D1-215
Speaker: Damian Sobota (University of 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 \(C(K\times K)\).
Room: D1-215
Speaker: Damian Sobota (University of 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 \(C(K\times K)\).