Several Inequalities for Khatri-Rao Products of Hilbert Space Operators - Ploymukda, Arnon; Chansangiam, Pattrawut (Communications in Mathematics and Applications, 2017)
We establish several inequalities for Khatri-Rao products of Hilbert space operators, involving ordinary products, ordinary powers, ordinary inverses, and Moore-Penrose inverses. Kantorovich type inequalities concerning Khatri-Rao products are also investigated. Our results generalize some matrix inequalities in the literature. In our case, we must impose some mild conditions on operators such as the closeness of their ranges. Furthermore, we develop new operator inequalities by using block partitioning technique and unital positive linear maps.
Keywords: Tensor product; Khatri-Rao product; Tracy-Singh product; Moore-Penrose inverse; Unital positive linear map