Schur idempotents and hyperreflexivity (Q502985)

The authors address the open question of whether the Boolean lattice \({\mathfrak C}\) generated by the set of all contractive Schur idempotents coincides with the set of all Schur idempotents. What they show is that every element of \({\mathfrak C}\) has a hyperreflexive range (Proposition 3.11 and Corollary 3.12). Thus, if one could find a Schur idempotent whose range is not hyperreflexive, then the open question would have a negative answer. Later sections of the paper provide results on the preservation of hyperreflexivity for sums, intersections, and tensor products of hyperreflexive masa-bimodules.