Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2604.26540 |
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Inhaltsangabe:
- We study bijections between the positive cones of spaces of continuous functions vanishing at infinity that satisfy a norm additive condition. Such maps arise naturally in the study of nonlinear functional equations and norm-preserving structures on function spaces. While in the compact (unital) case these maps can often be analyzed via linear extension techniques, the non-unital setting $C_0(X)$ requires a different approach due to the absence of a distinguished unit element. In this paper, we show that every bijection $T:C_0^+(X)\to C_0^+(Y)$ between the positive cones of $C_0(X)$ and $C_0(Y)$ satisfying \[ \|T(f+g)\|=\|Tf+Tg\| \] for all $f,g\in C_0^+(X)$ admits a representation of the form \[ Tf(y)=h(y)f(τ(y)), \] where $τ:Y\to X$ is a homeomorphism and $h$ is a bounded continuous function from $Y$ to $(0,\infty)$. This yields a complete characterization of norm additive bijections on positive cones of $C_0^+(X)$.