p-Quasihyponormal operators have scalar extensions of order 6

In this paper we show that every p-quasihyponormal operator has a scalar extension of order 6, i.e., is similar to the restriction to a closed invariant subspace of a scalar operator of order 6, where 0<p<1. As a corollary, we get that every p-quasihyponormal operator with rich spectra has a nontrivial invariant subspace. Also we show that Aluthge transforms preserve an analogue of the single-valued extension property for W²(D,H) and an operator T.