Product numerical range in a space with tensor product structure

Article, Preprint English OPEN
Puchała, Zbigniew ; Gawron, Piotr ; Miszczak, Jarosław Adam ; Skowronek, Łukasz ; Choi, Man-Duen ; Życzkowski, Karol (2011)
  • Publisher: Elsevier BV
  • Journal: Linear Algebra and its Applications, volume 434, issue 1, pages 327-342 (issn: 0024-3795)
  • Related identifiers: doi: 10.1016/j.laa.2010.08.026
  • Subject: Geometry and Topology | Mathematics - Operator Algebras | Numerical Analysis | Algebra and Number Theory | Discrete Mathematics and Combinatorics | Quantum Physics

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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