This is an announcement for the paper “A note on universal operators between separable Banach spaces” by Joanna Garbulińska-Wegrzynhttps://arxiv.org/search/math?searchtype=author&query=Garbuli%C5%84ska-Wegrzyn%2C+J, Wieslaw Kubiśhttps://arxiv.org/search/math?searchtype=author&query=Kubi%C5%9B%2C+W.

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.

https://arxiv.org/abs/1912.13312