Damina Sobota
Damina Sobota: On sequences of finitely supported measures on products of compact spaces
08/05/22 20:10
Tuesday, May 10, 2022 17:00
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Damina Sobota (KGRC, Vienna)
Title: On sequences of finitely supported measures on products of compact spaces
Abstract: Cembranos, Freniche, and Khurana (all independently) proved that for every two infinite compact spaces \(K\) and \(L\) the Banach space \(C(K\times L)\) contains a complemented copy of the space \(c_0\). To obtain this copy all the three proofs utilize in some way the Josefson-Nissenzweig theorem which more or less asserts that there is a sequence \((mu_n)\) of normalized signed Radon measures on \(K\times L\) such that \(mu_n(f)\) converges to \(0\) for every \(f\) from \(C(K\times L)\). Since most (if not all) of the known proofs of the J-N theorem are non-constructive, it follows that the (known to me) proofs of Cembranos et al. are also non-constructive. During my talk I'll show a generalization of the theorem of Cembranos et al. whose proof uses a direct construction of a sequence \((mu_n)\) of finitely supported measures on \(K\times L\) as above. I'll also discuss the case of pseudocompact spaces \(K\) and \(L\) and pose some questions.
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Damina Sobota (KGRC, Vienna)
Title: On sequences of finitely supported measures on products of compact spaces
Abstract: Cembranos, Freniche, and Khurana (all independently) proved that for every two infinite compact spaces \(K\) and \(L\) the Banach space \(C(K\times L)\) contains a complemented copy of the space \(c_0\). To obtain this copy all the three proofs utilize in some way the Josefson-Nissenzweig theorem which more or less asserts that there is a sequence \((mu_n)\) of normalized signed Radon measures on \(K\times L\) such that \(mu_n(f)\) converges to \(0\) for every \(f\) from \(C(K\times L)\). Since most (if not all) of the known proofs of the J-N theorem are non-constructive, it follows that the (known to me) proofs of Cembranos et al. are also non-constructive. During my talk I'll show a generalization of the theorem of Cembranos et al. whose proof uses a direct construction of a sequence \((mu_n)\) of finitely supported measures on \(K\times L\) as above. I'll also discuss the case of pseudocompact spaces \(K\) and \(L\) and pose some questions.