International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 362409, 6 pages
Research Article

Some Estimates of Certain Subnormal and Hyponormal Derivations

Vasile Lauric

Department of Mathematics, Florida A&M University, Tallahassee, FL 32307, USA

Received 23 October 2007; Accepted 9 January 2008

Academic Editor: Nils Ackermann

Copyright © 2008 Vasile Lauric. 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 prove that if A and B are subnormal operators and X is a bounded linear operator such that AXXB is a Hilbert-Schmidt operator, then f(A)XXf(B) is also a Hilbert-Schmidt operator and f(A)XXf(B)2LAXXB2 for f belongs to a certain class of functions. Furthermore, we investigate the similar problem in the case that S, T are hyponormal operators and X() is such that SXXT belongs to a norm ideal (J,J), and we prove that f(S)XXf(T)J and f(S)XXf(T)JCSXXTJ for f being in a certain class of functions.