Isometries on certain non-complete vector-valued function spaces

Mojahedi Mojtaba and Sady Fereshteh: Isometries on certain non-complete vector-valued function spaces. In: Acta scientiarum mathematicarum, (85) 3-4. pp. 613-627. (2019)

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Abstract

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.

Item Type:	Article
Journal or Publication Title:	Acta scientiarum mathematicarum
Date:	2019
Volume:	85
Number:	3-4
ISSN:	2064-8316
Page Range:	pp. 613-627
Related URLs:	http://acta.bibl.u-szeged.hu/66425/
DOI:	10.14232/actasm-018-092-6
Uncontrolled Keywords:	Valós lineáris izometriák, vektor-értékű függvényterek
Additional Information:	Bibliogr.: p. 626-627.
Date Deposited:	2020. Apr. 23. 14:06
Last Modified:	2021. Mar. 25. 15:34
URI:	http://acta.bibl.u-szeged.hu/id/eprint/66336

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