Product numerical range in a space with tensor product structure

TitleProduct numerical range in a space with tensor product structure
Publication TypeJournal Article
Year of Publication2011
AuthorsPuchała Z, Gawron P, Miszczak J, Skowronek Ł., Choi M-D, Życzkowski K
JournalLinear Algebra Appl.
Volume434
Pagination327–342
ISSN0024-3795
AbstractWe 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.