Fractional powers of hyponormal operators of Putnam type

Abstract

We are concerned with fractional powers of the so-called hyponormal operators of Putnam type. Under some suitable assumptions it is shown that if A, B are closed hyponormal linear operators of Putnam type acting on a complex Hilbert space ℍ, then D((A+B¯)α)=D(Aα)∩D(Bα)=D((A+B¯)∗α) for each α∈(0,1). As an application, a large class of the Schrödinger's operator with a complex potential Q∈Lloc1(ℝd)+L∞(ℝd) is considered.