On range cyclic operator algebras. II

If A is a range cyclic algebra then it is proved that the strong and the un iform topologies coincide on (Lat A)(perpendicular to) and every nonzero el ement of (Lat A)(perpendicular to) contains an atom of (Lat A)(perpendicula r to). Spectral properties of some non-normal operators in range cyclic alg ebras or commuting with such algebras are also studied. For a maximal invar iant subspace nl of A, A(star) (I - P-M) is shown to be strongly dense in B (M-perpendicular to).