Unique Hahn-Banach theorems for spaces of homogeneous polynomials

Abstract

We investigate certain norm and continuity conditions that provide us with 'unique Hahn-Banach Theorems' from P((n)c(0)) to P((n)l(infinity)) and from P-N(E-n) to P(E-n "). We show that there is a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on complex co to a, but there is no unique norm-presenting extension from P((3)c(0)) to P((3)l(infinity)).