International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 12, Pages 1925-1932

Fractional powers of hyponormal operators of Putnam type

Toka Diagana

Department of Mathematics, Howard University, 2441 Sixth Street NW, Washington, DC 20059, USA

Received 20 January 2005; Revised 12 April 2005

Copyright © 2005 Toka Diagana. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 , 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 QLloc1(d)+L(d) is considered.