International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 43013, 19 pages
Bitraces on Partial -Algebras
1Mathematics Section, The Abdus Salam International Centre for Theoretical Physics, P. O. Box 586, Miramare 34014, Trieste, Italy
2Department of Mathematics, University of Ibadan, Ibadan 200001, Oyo State, Nigeria
Received 12 March 2006; Revised 12 December 2006; Accepted 27 February 2007
Academic Editor: Lokenath Debnath
Copyright © 2007 G. O. S. Ekhaguere. 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.
Unbounded bitraces on partial -algebras are considered, a class of ideals defined by them is exhibited, and several relationships between certain commutants, bicommutants, and tricommutants associated with the -representations and -antirepresentations determined by the bitraces are established. Moreover, a notion of a partial -algebra of unbounded densely defined linear maps on a Hilbert space,
as a generalization of a -algebra, is introduced and a set of criteria for classifying such algebras by means of the type of bitraces that are defined on them is proposed.