turkmath.org

Let $M$ be a metric space. The Banach space $Lip(M)$ of real-valued Lipschitz functions defined on $M$ is a dual space, and its predual $F(M)$, called the free space over $M$, enjoys remarkable functorial properties. The free spaces are easy to define and useful, but so far their structure is not well-understood. We will investigate in particular when such spaces have the Grothendieck bounded approximation property, and relate this property with extension operators for Lipschitz functions.