  For a positive trace-class operator $C$ and a bounded operator $A$, we
provide an explicit description of the closure of the orbit-closed
$C$-numerical range of $A$ in terms of those operators submajorized by $C$ and
the essential numerical range of $A$. This generalizes and subsumes recent work
of Chan, Li and Poon for the $k$-numerical range, as well as some of our own
previous work on the orbit-closed $C$-numerical range.
