Operator Topologies and Invariant Operator Ranges

Abstract The invariant operator range lattices of a wide class of uniformly closed algebras (including C*-algebras) are stable under weak closures. There is an algebra whose invariant operator range lattice contains properly the corresponding lattice of its norm closure. An operator range transitive algebra is operator range n -transitive for all n. A normal operator is algebraic if and only if each of its invariant operator ranges is the range of some operator commuting with it.