Damian Głodkowski
Damian Głodkowski: A Banach space C(K) reading the dimension of K
08/11/22 05:58
Tuesday, November 8, 2022 17:00
Location: room C11-3.11
Speaker: Damian Głodkowski (University of Warsaw)
Title: A Banach space C(K) reading the dimension of K
Abstract: For every natural number \(n\) I construct (assuming Jensen's diamond principle) a compact space \(K_n\) such that whenever \(L\) is a compact space and the Banach spaces of continuous functions \(C(K_n)\) and \(C(L)\) are isomorphic, the covering dimension of \(L\) is equal to \(n\). The constructed space is a modification of Koszmider's example of a compact space \(K\) with the property that every bounded linear operator \(T\) on \(C(K)\) is a weak multiplication (i.e. it is of the form \(T(f)=gf+S(f)\), where \(g\) is an element of \(C(K_n)\) and \(S\) is weakly compact). In the talk I will give a sketch of the construction and focus on the differences between my and the original space. The talk will be based on https://arxiv.org/abs/2207.00149.
Location: room C11-3.11
Speaker: Damian Głodkowski (University of Warsaw)
Title: A Banach space C(K) reading the dimension of K
Abstract: For every natural number \(n\) I construct (assuming Jensen's diamond principle) a compact space \(K_n\) such that whenever \(L\) is a compact space and the Banach spaces of continuous functions \(C(K_n)\) and \(C(L)\) are isomorphic, the covering dimension of \(L\) is equal to \(n\). The constructed space is a modification of Koszmider's example of a compact space \(K\) with the property that every bounded linear operator \(T\) on \(C(K)\) is a weak multiplication (i.e. it is of the form \(T(f)=gf+S(f)\), where \(g\) is an element of \(C(K_n)\) and \(S\) is weakly compact). In the talk I will give a sketch of the construction and focus on the differences between my and the original space. The talk will be based on https://arxiv.org/abs/2207.00149.