Product numerical range in a space with tensor product structure

Details Product numerical range in a space with tensor product structure Product numerical range in a space with tensor product structure

2010-08-20

arxiv.org/abs/1008.3482v1

Linear Algebra Appl., 434 (2011) 327-342

Mathematics

Operator Algebras

17 pages, 4 figures. Original preprint "Local numerical range: a versatile tool in the theory of quantum information" [arXiv:0

Scientific paper

10.1016/j.laa.2010.08.026

We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived. Product numerical range of a non-Hermitian operator forms a subset of the standard numerical range containing the barycenter of the spectrum. While the latter set is convex, the product range needs not to be convex nor simply connected. The product numerical range of a tensor product is equal to the Minkowski product of numerical ranges of individual factors.

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