Banach spaces with the Daugavet property

Vladimir Kadets, Roman Shvidkoy, Gleb Sirotkin +1

A Banach space $X$ is said to have the Daugavet property if every operator $T:X\to X$ of rank~$1$ satisfies $\Vert Id+T\Vert =1+\Vert T\Vert$. We show that then every weakly compact operator s…