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International Journal of Mathematics and Mathematical Sciences
Volume 2007, Article ID 43013, 19 pages
Research Article

Bitraces on Partial O*-Algebras

1Mathematics Section, The Abdus Salam International Centre for Theoretical Physics, P. O. Box 586, Miramare, Trieste 34014, Italy
2Department of Mathematics, University of Ibadan, Ibadan, Oyo State 200001, 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 O*-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 W*-algebra of unbounded densely defined linear maps on a Hilbert space, as a generalization of a W*-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.