Isometries on certain non-complete vector-valued function spaces
Surjective, not necessarily linear isometries T: AC(X, E)→AC(Y, F) between vector-valued absolutely continuous functions on compact subsets X and Y of the real line have recently been described as generalized weighted composition operators. The target spaces E and F are strictly convex normedspaces....
Elmentve itt :
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| Dokumentumtípus: | Cikk |
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2019
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| Sorozat: | Acta scientiarum mathematicarum
85 No. 3-4 |
| Kulcsszavak: | Valós lineáris izometriák, vektor-értékű függvényterek |
| doi: | 10.14232/actasm-018-092-6 |
| Online Access: | http://acta.bibl.u-szeged.hu/66336 |
| Tartalmi kivonat: | Surjective, not necessarily linear isometries T: AC(X, E)→AC(Y, F) between vector-valued absolutely continuous functions on compact subsets X and Y of the real line have recently been described as generalized weighted composition operators. The target spaces E and F are strictly convex normedspaces. In this paper, we assume that X and Y are compact Hausdorff spaces and E and F are normed spaces, which are not assumed to be strictly convex. We describe (with a short proof) surjective isometries T:(A,‖·‖A)→(B,‖·‖B) between certain normed subspaces A and B of C(X, E)and C(Y, F), respectively. We consider three cases for F with some mild conditions. The first case, in particular, provides a short proof for the above result, without assuming that the target spaces are strictly convex. The other cases give some generalizations in this topic. As a consequence, the results can be applied, for isometries (notnecessarily linear) between spaces of absolutely continuous vector-valued func-tions, (little) Lipschitz functions and also continuously differentiable functions. |
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| Terjedelem/Fizikai jellemzők: | 613-627 |
| ISSN: | 2064-8316 |