Filip Talimdjioski

will speak on

Lipschitz-free spaces over Cantor sets and approximation properties

Time: 3:00PM
Date: Tue 11th April 2023
Location: Seminar Room SCN 1.25 [map]

Further information

Abstract: Let $K=2^\mathbb{N}$ be the Cantor set, let $\mathcal{M}$ be the set of all metrics $d$ on $K$ that give its usual (product) topology, and equip $\mathcal{M}$ with the topology of uniform convergence, where the metrics are regarded as functions on $K^2$. In this talk we show that the set of metrics $d\in\mathcal{M}$ for which the Lipschitz-free space $\mathcal{F}(K,d)$ has the metric approximation property is a residual $F_{\sigma\delta}$ set in $\mathcal{M}$, and that the set of metrics $d\in\mathcal{M}$ for which $\mathcal{F}(K,d)$ fails the approximation property is a dense meager set in $\mathcal{M}$. Time allowing, we will also use the notion of Hausdorff dimension to show the existence of a family $(d_\alpha)\subseteq\mathcal{M}$ of size continuum, such that $\mathcal{F}(K,d_\alpha)$ and $\mathcal{F}(K,d_\beta)$ are not isomorphic as algebras for $\alpha\not= \beta$.


https://ucd-ie.zoom.us/j/65456653274

https://ucd-ie.zoom.us/j/65456653274

(This talk is part of the Analysis series.)

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