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Bounds on polygons of higher rank numerical ranges. (English) Zbl 1312.15026
Summary: Research in higher rank numerical ranges has originally been motivated by problems in quantum information theory, particularly in quantum error correction. The higher rank numerical range generalizes the classical numerical range of an operator. The higher rank numerical range is typically not a polygon, however when we consider normal operators the higher rank numerical range is a polygon in the complex plane \(\mathbb{C}\). In this article, we give a new proof of an upper bound on the number of sides of the higher-rank numerical range of a normal operator and we also find a lower bound for the number of sides of the higher-rank numerical range of a unitary operator. We show that these bounds are the best possible.
MSC:
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
47A12 Numerical range, numerical radius
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