Some norm inequalities concerning generalized inverses, 2

We extend to the von Neumann–Schatten classes Cp and norms ∥·∥p, where 2 ⩽ p < ∞, Penrose’s result on minimizing ∥AXB − C∥2. We give an example to show that this extension does not hold for 1 ⩽ p < 2. The proof of the global inequality depends on local considerations.