HERMITIAN OPERATORS ON SPACES OF VECTOR-VALUED LIPSCHITZ MAPS (Researches on theory of isometries and preserver problems from a various point of view)

Abstract

We characterize unital surjective linear isometries on algebra of Lipschitz maps with the values in matrix algebras with the ell_{1} norm Vert. Vert_{infty}+L(cdot). The fact that Hermitian operators completely characterizes unital surjective linear isometries lets us prove this. The method is sometime referred to as Lumer's method (see [5]). To apply Lumer's method, one needs to characterize Hermitian operators.