A note on universal operators between separable Banach spaces
| Autor: | Garbulińska-Wegrzyn, Joanna, Kubiś, Wieslaw |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Rev. R. Acad. Cienc. Exactas F\'is. Nat. Ser. A Math. RACSAM 114 (2020), Article number: 148 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s13398-020-00878-4 |
| Popis: | We compare two types of universal operators constructed relatively recently by Cabello S\'anchez, 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. Comment: 12 pages |
| Databáze: | arXiv |
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