On diagonalizable operators in Minkowski spaces with the Lipschitz property

semi-inner-product space is a real vector space M equipped with a function [.,.]:M×M→R which is linear in its first variable, strictly positive and satisfies the Schwartz inequality. It is well known that the function defines a norm on M and vice versa, for every norm on X there is a semi-inner-product satisfying this equality. A linear operator A on M is called adjoint abelian with respect to [.,.], if it satisfies [Ax,y]=[x,Ay] for every x,y∈M. The aim of this paper is to characterize the diagonalizable adjoint abelian operators in finite dimensional real semi-inner-product spaces satisfying a certain smoothness condition.