A norm inequality for pairs of commuting positive semidefinite matrices

الأصل · EN

For k=1,,K, let Aₖ and Bₖ be positive semidefinite matrices such that, for each k, Aₖ commutes with Bₖ. We show that, for any unitarily invariant norm, |||∑ₖ₌₁ᵏ AₖBₖ||| ≤ ||| (∑ₖ₌₁ᵏ Aₖ)(∑ₖ₌₁ᵏ Bₖ)|||.