The k-rank numerical radii

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

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