  Let $C_1(H)$ denote the space of all trace class operators on an arbitrary
complex Hilbert space $H$. We prove that $C_1(H)$ satisfies the
$\lambda$-property, and we determine the form of the $\lambda$-function of Aron
and Lohman on the closed unit ball of $C_1(H)$ by showing that $$\lambda (a) =
\frac{1 - \|a\|_1 + 2 \|a\|_{\infty}}{2},$$ for every $a$ in ${C_1(H)}$ with
$\|a\|_1 \leq 1$. This is a non-commutative extension of the formula
established by Aron and Lohman for $\ell_1$.
