Perspectivity in projection lattices
Peter Fillmore · Proceedings of the American Mathematical Society · 1965
Let A be a w*-algebra and L its projection lattice.It is well known [3] that projections perspective in L are linked by a partial isometry in A, and that these two notions coincide precisely when the algebra A is finite.We show in this paper that, in any w*-algebra, perspectivity enjoys virtually every property, other than additivity, of the relation ~ of partial isometry equivalence.These properties are