The Daugavet equation for polynomials on -algebras

In this paper, we study the Daugavet equation and the alternative Daugavet equation for polynomials on C ∗ -algebras. We study separately the cases in which the C ∗ -algebras are commutative and non-commutative. In these cases, we obtain necessary and sufficient conditions on such C ∗ -algebras in order that certain polynomial classes satisfy the Daugavet equation and the alternative Daugavet equation.