On the higher rank numerical range of the shift

Details On the higher rank numerical range of the shift On the higher rank numerical range of the shift

2010-05-03

arxiv.org/abs/1005.0391v1

Mathematics

Functional Analysis

Scientific paper

For any n-by-n complex matrix T and any $1\leqslant k\leqslant n$, let $\Lambda_{k}(T)$ the set of all $\lambda\in \C$ such that $PTP=\lambda P$ 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 $\cos\dfrac{k\pi}{n+1}$ if $1

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