Cauchy-Schwarz inequalities associated with positive semidefinite matrices

AbstractUsing a quasilinear representation for unitarily invariant norms, we prove a basic inequality: Let A=LXX∗M be positive semidefinite, where X∈Mm,n. Then |||X|p||2⩽‖Lp‖ ‖Mp‖ for all p>0 and all unitarily invariant norms ‖·‖. We show how several inequalities of Cauchy-schwarz type follow from this bound and obtain a partial analog of our results for lp norms