A note on universal operators between separable Banach spaces

Joanna Garbulińska-Wȩgrzyn, Wiesław Kubiś
2020 RACSAM  
We compare two types of universal operators constructed relatively recently by Cabello Sánchez, and the authors. The first operator acts on the Gurariȋ space, while the second one P S has values in a fixed separable Banach space S. We show that if S is the Gurariȋ 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 is generic in the sense of a natural infinite game.
doi:10.1007/s13398-020-00878-4 fatcat:fp7pzkfblrd6ll6lnbgti3xuae