Relations between principal functions of \bm{p}-hyponormal operators

Dedicated to Professor Sin-Ei Takahasi on his sixtieth birthday

Abstract

Let T =U|T| be a bounded linear operator with the associated polar decomposition on a separable infinite dimensional Hilbert space. For 0 < t < 1, let T_t =|T|^tU|T|^1-t and \fg_T and \fg_{T_t} be the principal functions of T and T_t, respectively. We show that, if T is an invertible semi-hyponormal operator with trace class commutator [|T|, U], then \fg_T =\fg_{T_t} almost everywhere on \bm{C}. As a biproduct we reprove Berger's theorem and index properties of invertible p-hyponormal operators.