Alberto Salguero Alarcón
Alberto Salguero Alarcón: A twisted sum of \(C(K)\)-spaces not isomorphic to any \(C(K)\)-space
15/10/21 07:17
Tuesday, October 19, 2021 17:00
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Alberto Salguero Alarcón (Universidad de Extremadura, Badajoz, Spain)
Title: A twisted sum of \(C(K)\)-spaces not isomorphic to any \(C(K)\)-space
Abstract: A twisted sum of two Banach spaces \(X\) and \(Y\) is another space \(Z\) containing \(Y\) as a closed subspace so that \(Z/Y=X\). In this talk we focus on twisted sums of spaces of continuous functions on compact spaces. It has been known for some time that a twisted sum of two \(C(K)\)-spaces does not need to be isomorphic to a \(C(K)\)-space. We will focus on one recent and singular construction which serves as an example: a twisted sum of \(c_0\) and \(c_0(\mathfrak c)\) which is not isomorphic to any \(C(K)\)-space. This is part of a joint work with Grzegorz Plebanek.
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Alberto Salguero Alarcón (Universidad de Extremadura, Badajoz, Spain)
Title: A twisted sum of \(C(K)\)-spaces not isomorphic to any \(C(K)\)-space
Abstract: A twisted sum of two Banach spaces \(X\) and \(Y\) is another space \(Z\) containing \(Y\) as a closed subspace so that \(Z/Y=X\). In this talk we focus on twisted sums of spaces of continuous functions on compact spaces. It has been known for some time that a twisted sum of two \(C(K)\)-spaces does not need to be isomorphic to a \(C(K)\)-space. We will focus on one recent and singular construction which serves as an example: a twisted sum of \(c_0\) and \(c_0(\mathfrak c)\) which is not isomorphic to any \(C(K)\)-space. This is part of a joint work with Grzegorz Plebanek.