2010/08/20 by Zbigniew Puchała, Piotr Gawron, Jarosław Adam Miszczak +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #math.OA #quant-ph
paper · pdf · doi:10.1016/j.laa.2010.08.026
published as Linear Algebra Appl., 434 (2011) 327-342 · 17 pages, 4 figures. Original preprint "Local numerical range: a versatile tool in the theory of quantum information" [arXiv:0905.3646v1] was broadened and split into two papers: "Restricted numerical range: a versatile tool in the theory of quantum information", and "Product numerical range in a space with tensor product structure"
arxiv created 2010/08/20 · openalex publication_date 2010/09/21 · crossref created 2010/09/21 · arxiv updated 2010/11/01 · crossref issued 2011/01/01 · crossref published 2011/01/01 · crossref published-print 2011/01/01 · crossref deposited 2021/11/10 · openalex created_date 2025/10/10 · crossref indexed 2026/05/21 · openalex updated_date 2026/07/28
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.