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.

Tags: Damian Głodkowski