Open projections and Murray–von Neumann equivalence

Abstract

AbstractWe characterize the ‐algebras for which openness of projections in their second duals is preserved under Murray–von Neumann equivalence. They are precisely the extensions of commutative ‐algebras by annihilator ‐algebras. We also show that the annihilator ‐algebras are precisely the ‐algebras for which all projections in their second duals are open.