International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 9, Pages 573-582
Putnam-Fuglede theorem and the range-kernel orthogonality of derivations
Department of Mathematics, Faculty of Science, United Arab Emirates University, P.O. Box 17551, Al Ain, United Arab Emirates
Received 3 November 2000
Copyright © 2001 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.
Let denote the algebra of operators on a Hilbert
space into itself. Let or , where is the generalized derivation and is the elementary operator . Given , we say that the pair has the property if implies . This paper characterizes operators , and for which the pair has property , and establishes a relationship between the -property of the pair and the range-kernel orthogonality of the operator .