International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 3, Pages 465-474
doi:10.1155/IJMMS.2005.465
Subspace gaps and Weyl's theorem for an elementary operator
Department of Mathematics and Computer Science, Faculty of Science, United Arab Emirates University, P.O. Box 17551, Al-Ain, United Arab Emirates
Received 25 July 2004
Copyright © 2005 B. P. Duggal. 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.
Abstract
A range-kernal orthogonality property is established for the elementary operators ℰ(X)=∑i=1nAiXBi and ℰ*(X)=∑i=1nAi*XBi*, where A=(A1,A2,…,An) and B=(B1,B2,…,Bn) are n-tuples of mutually commuting scalar operators (in the sense of Dunford) in the algebra B(H) of operators on a Hilbert space H. It is proved that the operator ℰ satisfies Weyl's theorem in the case in which A and B are n-tuples of mutually commuting generalized scalar operators.