Gurarii operators are generic

Abstract

Answering a question of Garbulińska-Wȩgrzyn and Kubiś, we prove that Gurarii operators form a dense $G_{\delta }$-set in the space $\mathcal{B}(\mathbb{G})$ of all nonexpansive operators on the Gurarii space $\mathbb{G}$, endowed with the strong operator topology. This implies that the set of universal operators on $\mathbb{G}$ form a residual set in $\mathcal{B}(\mathbb{G})$.

12 pages