Remarks on the Murray-von Neumann Equivalence of Projections
Bernard M. Nzimbi *
Department of Mathematics, Faculty of Science and Technology, University of Nairobi, P.O. Box 30197 - 00100, Nairobi, Kenya.
B. N. Kiratu
Department of Pure and Applied Mathematics, Faculty of Applied Sciences and Technology, Technical University of Kenya, P.O. Box 52428 - 00200, Nairobi, Kenya.
I. N. Sitati
Garissa University College, P.O. Box 1801-70100, Garissa, Kenya.
S. Towett
Department of Mathematics, Faculty of Science and Technology, University of Nairobi, P.O. Box 30197 - 00100, Nairobi, Kenya.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we characterize Murray-von Neumann equivalent projections. We also investigate and compare the relationship between the Murray von Neumann relation and other equivalence relations on the set P (B (H)) of orthogonal projections in the von Neumann algebra B (H).
Keywords: Partial isometry, orthogonal projection, Murray-von Neumann equivalence, unitary equivalence, metric equivalence, central carrier