The k-rank numerical radii
  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 $A$. 
Aikaterini Aretaki, John Maroulas
math.FA