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We study hermitian operators and isometries on spaces of vector-valuedLipschitz maps with the sum norm: $\|\cdot\|_{\infty}+L(\cdot)$. There are twomain theorems in this paper. Firstly, we prove that every hermitian operator on$\operatorname{Lip}(X,E)$, where $E$ is a complex Banach space, is ageneralized composition operator. Secondly, we give a complete description ofunital surjective complex linear isometries on$\operatorname{Lip}(X,\mathcal{A})$ where $\mathcal{A}$ is a unital factor$C^{*}$-algebra. These results improve previous results stated by the author.

Isometries and hermitian operators on spaces of vector-valued Lipschitz maps