1. CMB 2016 (vol 60 pp. 196)
2. CMB 2000 (vol 43 pp. 193)
 Magajna, Bojan

C$^*$Convexity and the Numerical Range
If $A$ is a prime C$^*$algebra, $a \in A$ and $\lambda$ is in the
numerical range $W(a)$ of $a$, then for each $\varepsilon > 0$ there
exists an element $h \in A$ such that $\norm{h} = 1$ and $\norm{h^*
(a\lambda)h} < \varepsilon$. If $\lambda$ is an extreme point of
$W(a)$, the same conclusion holds without the assumption that $A$ is
prime. Given any element $a$ in a von Neumann algebra (or in a
general C$^*$algebra) $A$, all normal elements in the weak* closure
(the norm closure, respectively) of the C$^*$convex hull of $a$ are
characterized.
Categories:47A12, 46L05, 46L10 
