Reflexive *-derivations and lattices of invariant subspaces of operator algebras associated with them

The paper studies unbounded reflexive *-derivations δ of C*-algebras of bounded operators on Hilbert spaces H whose domains D(δ) are weekly dense in B(H and contain compact operators. It describes a one-to-one correspondence between these derivations and pairs S,L, where S are symmetric densely operators on H and L are J-orthogonal π-reflexive lattices of subspaces in the deficiency spaces of S. The domains D(δ) of these *-derivations are associated with some non-selfadjoint reflexive algebras Aδ of bounded operators on H⊕H. The paper analyzes the structure of the lattices of invariant subspaces of Aδ and of the normalizers of Aδ-the largest Lie subalgebras of B(H⊕H) such that Aδ are their Lie ideals.