Hermitian operators and isometries on algebras of matrix-valued Lipschitz maps

This paper deals with hermitian operators and surjective linear isometries, between spaces of Lipschitz maps, defined on a compact metric space, with values in a finite dimensional vector space. These spaces are endowed with the sum norm. The first main result formulates that hermitian operators are composition operators (Theorem 2.2) and the second one (Theorem 3.3) gives a characterization for the surjective unital linear isometries between Banach algebras of Lipschitz maps with values in M-n(C).