On the Mazur--Ulam property for the space of Hilbert-space-valued continuous functions

María Cueto-Avellaneda, Antonio M. Peralta

Let $K$ be a compact Hausdorff space and let $H$ be a real or complex Hilbert space with dim$(H_{\mathbb{R}})\ge 2$. We prove that the space $C(K,H)$ of all $H$-valued continuous fu…