Equação de Daugavet para polinômios

Abstract

In this work we will study the Daugavet Equation and the Alternative Daugavet Equation for bounded functions on Banach spaces. Firstly we will present characterizations of these equations for bounded functions and uniformly continuous functions. Next we will study such equations for polynomials and holomorphic mappings on Banach spaces, especially on spaces of continuous functions. We will also study the k-order Daugavet property and the k-order alternative Daugavet property. And finally we will show some results about the stability of the polynomial Daugavet property and the alternative polynomial Daugavet property.