TITLE: An extreme point of the ball of the space of compact operators
QUESTION [5 upvotes]: It is very easy to see that the unit ball of $c_0$ has no extreme points. I was trying to spot any extreme points in the unit ball of the space of compact operators on a Hilbert space (a non-commutative version of $c_0$) but without success.

Does the unit ball of $K(\ell_p)$ have any extreme points for some $p\in (1,\infty)$?

REPLY [8 votes]: For $p\neq 2$ there are plenty of extreme points in $K(\ell_p)$.
J. Hennefeld, Compact extremal operators, Il. J. Math. 21 (1977) 61-65.