01088nas a2200205   4500000000100000000000100001000000100002008004100003100002200044700001700066700002200083700001800105700001800123700002200141245006900163300001400232490000800246520061400254022001400868       2011                            d1 aZbigniew Puchała1 aPiotr Gawron1 aJaroslaw Miszczak1 aŁ. Skowronek1 aMan-Duen Choi1 aKarol Życzkowski00aProduct numerical range in a space with tensor product structure  a327–3420 v4343 aWe 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.  a0024-3795