On density of algebras with minimal invariant operator ranges

Abstract

Let A \mathfrak {A} be an arbitrary subalgebra of B ( H ) \mathcal {B}(\mathcal {H}) and let M \mathfrak {M} be a dense operator range invariant under A \mathfrak {A} such that every nonzero operator range invariant under A \mathfrak {A} contains M \mathfrak {M} . Then the closure of A \mathfrak {A} in the strong operator topology is B ( H ) \mathcal {B}(\mathcal {H}) .