Strictly convex renormings and the diameter 2 property
| Autor: | Nygaard, Olav, Põldvere, Märt, Troyansky, Stanimir, Viil, Tauri |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A Banach space (or its norm) is said to have the diameter $2$ property (D$2$P in short) if every nonempty relatively weakly open subset of its closed unit ball has diameter $2$. We construct an equivalent norm on $L_1[0,1]$ which is weakly midpoint locally uniformly rotund and has the D$2$P. We also prove that for Banach spaces admitting a norm-one finite-co-dimensional projection it is impossible to be uniformly rotund in every direction and at the same time have the D$2$P. Comment: 12 pages |
| Databáze: | arXiv |
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