On the higher rank numerical range of the shift

2010/05/03 by Haykel Gaaya, Gaaya, Haykel
Mathematics · Computer Science · #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1005.0391

Abstract

For any n-by-n complex matrix T and any 1\leqslant k\leqslant n, let Λ_k(T) the set of all λ∈ \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 \Cⁿ then its rank-k numerical range is the circular disc centred in zero and with radius cos\dfrackπn+1 if 1

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