On the higher rank numerical range of the shift operator
Haykel Gaaya · arXiv (Cornell University) · 2010
For any n-by-n complex matrix T and any $1\leqslant k\leqslant n$, let $Λ_{k}(T)$ the set of all $λ\in \C$ such that $PTP=λP$ for some rank-k orthogonal projection $P$ be its higher rank-k numerical range. It is shown that if $\bbS$ is the n-dimensional shift on ${\C}^{n}$ then its rank-k numerical range is the circular disc centred in zero and with radius $\cos\dfrac{kπ}{n+1}$ if $1