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

The paper studies unbounded reflexive *-derivations of C*-algebras of bounded operators on Hilbert spaces H whose domains D( ) 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 -reflexive lattices of subspaces in the deficiency spaces of S. The domains D( ) of these *-derivations are associated with some non-selfadjoint reflexive algebras A of bounded operators on H ⊕ H. The paper analyzes the structure of the lattices of invariant subspaces of A and of the normalizers of A -the largest Lie subalgebras of B(H ⊕ H) such that A are their Lie ideals. © 2005 Elsevier Inc. All rights reserved.