Gurarii operators are generic

TL;DR

This paper proves that Gurarii operators are topologically generic in the space of all nonexpansive operators on the Gurarii space, indicating that universal operators are prevalent in this setting.

Contribution

It establishes that Gurarii operators form a dense G_delta set in the space of nonexpansive operators, answering a question about their genericity.

Findings

Gurarii operators form a dense G_delta set in the space of nonexpansive operators.

The set of universal operators on the Gurarii space is residual.

This confirms the genericity of Gurarii operators in the strong operator topology.

Abstract

Answering a question of Garbuli\'nska-W\c{e}grzyn and Kubi\'s, 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 $\mathcal B(\mathbb G)$.