On range tripotents in JBW*-triples

摘要

Let B be a JBW*-triple, let A be a JB*-subtriple of B and let R(A){mathcal{R}}(A) be the set of range tripotents relative to A. It is shown that, under certain conditions, the supremum of a family of range tripotents in R(A){mathcal{R}}(A) coincides with that in the complete lattice [(U)tilde](B)tilde{mathcal{U}}(B) of all tripotents in B. As a consequence, a sufficient condition for a tripotent to be a range tripotent relative to A is obtained. The action of isomorphisms on range tripotents is investigated, and an analysis of the suprema of families of spectral range tripotents leads to a generalization of a result known for open projections in W*-algebras.