$p$-hyponormal operators are subscalar

Abstract

We prove that if R, S ∈ B(X), R,S are injective, then RS is subscalar if and only if SR is subscalar. As corollaries, it is shown that phyponormal operators (0 < p ≤ 1) and log-hyponormal operators are subscalar; also w-hyponormal operators T with KerT ⊂ KerT * and their generalized Aluthge transformations T (r, 1 − r) (0 < r < 1) are subscalar.