Let H N = H K ⊗ ⊗ H M be a tensor product Hilbert space. We define the product numerical radius r ⊗ ⊗ ( X ) of X , with respect to this tensor product structure, as r ⊗ ⊗ ( X ) = max { | z | : z ∈ ∈ Λ Λ ⊗ ⊗ ( X ) } .