Cones and norms in the tensor product of matrix spaces.
In the tensor product \({\mathbb M}_{n,m}\) of two matrix spaces \({\mathbb M}_m\) and \({\mathbb M}_n\) three natural cones are considered. The first one \({\mathcal P}_0\) consists of positive semi-definite matrices; the second one \({\mathcal P_+}\) is generated by tensor products of positive semi-definite matrices in the factor spaces; \({\mathcal P_-}\) is defined as the dual cone for~\({\mathcal P}_+\). In~\({\mathbb M}_{n,m}\) several tensor norms generated by spectral and/or trace norms in the factor space are considered. The author studies relationships among these norms as well as relations among the three kinds of order intervals in the tensor product.
scientific article; zbMATH DE number 2056675