| Starting from Daugavet's (1963) result stating that every compact linear operator T on C[0,1] satisfies the norm equality
||Id + T || = 1 + ||T||,
many results have been obtained on the spaces satisfying this isometric property (nowadays called the Daugavet property). This property can be characterized in term of the geometry of the Banach space and, actually, it can be viewed as a property that is extremely opposite of the Radon-Nikodym property.
In this talk we will give an introduction to known results about the Daugavet property and we will present a purely geometric description of it in the setting of C*-algebras, von Neumann preduals and Lindenstrauss spaces.
Some possiblegeneralizations and open problems will be also explored. |