2-local isometries on function spaces
| Autor: | Hatori, Osamu, Oi, Shiho |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study 2-local reflexivity of the set of all surjective isometries between certain function spaces. We do not assume linearity for isometries. We prove that a 2-local isometry in the group of all surjective isometries on the algebra of all continuously differentiable functions on the closed unit interval with respect to several norms is a surjective isometry. We also prove that a 2-local isometry in the group of all surjective isometries on the Banach algebra of all Lipschitz functions on the closed unit interval with the sum-norm is a surjective isometry. Comment: 22 pages |
| Databáze: | arXiv |
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