On extreme contractions and vertices in operator spaces

The investigations of the extreme points of the closed unit ball in spaces of operators were started by Kadison (1954) considering the operator space $\mathcal L(H)$. Grząślewicz (1997) considered the vertices of subsets of $\mathcal L(H)$. In this paper, motivated by more recent results, we investigate the extreme points and vertices in $\mathcal L(\ell _{\infty }^n,\ell _{1}^m)$, $\mathcal L(c_0,\ell _{1})$ and $\mathcal L(\ell _{1})$.