Some Non-linear geometrical properties of banach spaces

Abstract

In this survey we report on very recent results about some non-linear geometrical properties of many classes of real and complex Banach spaces and uniform algebras, including the ball algebra A u (B X) of all uniformly continuous functions on the closed unit ball and holomorphic on the open unit ball of a complex Banach spaceX. These geometrical properties are: Polynomial numerical index, Polynomial Daugavet property and Bishop-Phelp-Bollobás property for multilinear mappings.