This is an announcement for the paper Isometries on Banach algebras of vector-valued maps” by Osamu Hatorihttps://arxiv.org/find/math/1/au:+Hatori_O/0/1/0/all/0/1, Shiho Oihttps://arxiv.org/find/math/1/au:+Oi_S/0/1/0/all/0/1.

Abstract: One of the purposes of this paper is to propose a unified approach for studies on isometries on the algebras of Lipschitz maps and continuously differentiable maps. We describe isometries on a certain admissible quadruple which is a common generalization of the algebra of Lipschitz maps and the algebra of continuously differentiable maps with values in unital commutative $C^*$-algebras. It implies that the isometry in Example 8 in \cite{jp} is indeed canonical.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1709.05782