A note on universal operators between separable Banach spaces

Abstract

We compare two types of universal operators constructed relatively recently by Cabello Sánchez, and the authors. The first operator $\Omega$ acts on the Gurarii space, while the second one $P_S$ has values in a fixed separable Banach space $S$. We show that if $S$ is the Gurarii space, then both operators are isometric. We also prove that, for a fixed space $S$, the operator $P_S$ is isometrically unique. Finally, we show that $\Omega$ is generic in the sense of a natural infinite game.

12 pages

References in corpus (4)

• Quasi-Banach spaces of almost universal disposition
• A universal operator on the Gurarii space
• Game-theoretic characterization of the Gurarii space
• A separable Fréchet space of almost universal disposition