Abstract
Let $C^1([0,1], A)$ be the Banach algebra of all continuously differentiable maps from the closed unit interval $[0,1]$ to a uniform algebra $A$ with respect to certain norms. We prove that every surjective, not necessarily linear, isometry on $C^1([0,1], A)$ is represented by homeomorphisms on $[0,1]$ and the maximal ideal space of $A$.
Citation
Hironao Koshimizu. Takeshi Miura. "Surjective isometries on $C^1$ spaces of uniform algebra valued maps." Nihonkai Math. J. 30 (2) 41 - 76, 2019.
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