Murray–von Neumann equivalence

Summary

Murray–von Neumann equivalence is the basic way to compare projections in a C*-algebra or a von Neumann algebra. Two projections are equivalent when a partial isometry of the algebra maps the range of one onto the range of the other. In von Neumann algebras it is the tool behind the Murray–von Neumann classification of factors. In C*-algebras it is the relation used to define the group K0.