Strongly compact algebras.
An algebra of bounded linear operators on a Hilbert space is said to be if its unit ball is relatively compact in the strong operator topology. A bounded linear operator on a Hilbert space is said to be if the algebra generated by the operator and the identity is strongly compact. This notion was introduced by Lomonosov as an approach to the invariant subspace problem for essentially normal operators. First of all, some basic properties of strongly compact algebras are established. Next, a characterization...