The k-rank numerical radii

Abstract

The $k$-rank numerical range ${\Lambda }_k(A)$ is expressed via an intersection of a countable family of numerical ranges $\{F(M_{\nu }^{\ast }A{M}_{\nu }){\}}_{\nu \in \mathbb{N}}$ 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 $A$.

9 pages, 2 figures. To appear in Annals of Functional Analysis, 2012