Extreme polynomials on C-0

Abstract

We prove that every monomial in P((m)c(0)) is a strong extreme point of the unit ball of P((m)c(0)) in the complex case, and show that in P((2)c(0)) there is an extremal but not extreme polynomial in the real case. Moreover, we show that there is no extremal polynomial in P((m)c(0)) in the complex case.