Inequalities for the block projection operators

Abstract

Originally studied by Gohberg and Krein, the block projection operators admit a natural extension to the setting of quasi-normed ideals and noncommutative integration. Here, we establish several uniform submajorizationinequalities for block projection operators. We also show that in the quasi-normed setting, for $L_p$-spaces with $0 (p \leq 1$, a reverse inequality holds.