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arXiv · 2503.05097

Surjective isometries on function spaces with derivatives

M. G. Cabrera-Padilla·A. Jiménez-Vargas·Takeshi Miura·Moisés Villegas-Vallecillos
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Abstract

Let $A$ be a complex Banach space with a norm $\|f\|=\|f\|_X+\|d(f)\|_Y$ for $f\in A$, where $d$ is a complex linear map from $A$ onto a Banach space $B$, and $\|\cdot\|_K$ represents the supremum norm on a compact Hausdorff space $K$. In this paper, we characterize surjective isometries on $(A,\|\cdot\|)$, which may be nonlinear. This unifies former results on surjective isometries between specific function spaces.

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M. G. Cabrera-Padilla, A. Jiménez-Vargas, Takeshi Miura, Moisés Villegas-Vallecillos. 2025-03-07. Surjective isometries on function spaces with derivatives. https://arxiv.org/abs/2503.05097

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