Here we see that the p-Ces

ro operators, the generalized Ces

ro operators of order one, the discrete generalized Ces

ro operators, and their adjoints are all posinormal operators on

, but many of these operators are not dominant, not normaloid, and not spectraloid. The question of dominance for

, the generalized Ces

ro operators of order one, remains unsettled when

<1, and that points to some general questions regarding terraced matrices. Sufficient conditions are given for a terraced matrix to be normaloid. Necessary conditions are given for terraced matrices to be dominant, spectraloid, and normaloid. A very brief new proof is given of the well-known result that

is hyponormal when

.