Many properties of nest
algebras are actually valid for reflexive operator algebras with a commutative
subspace lattice. In this paper we collect a number of such results related to the
carrier space of the algebra. Included among these results are a generalization of
Ringrose’s criterion, a description of the partial correspondence between lattice
homomorphisms of the carrier space and projections in the lattice, the construction
of isometric representations of certain quotient algebras, and a direct sum
decomposition of the commutant of the core modulo the intersection of the spectral
ideals.
