  The $k$-rank numerical range $\Lambda_{k}(A)$ is expressed via an
intersection of a countable family of numerical ranges
$\{F(M^{*}_{\nu}AM_{\nu})\}_{\nu\in\mathbb{N}}$ with respect to $n\times
(n-k+1)$ isometries $M_{\nu}$. This implication for $\Lambda_{k}(A)$ provides
further elaboration of the $k$-rank numerical radii of $A$.
