Abstract
This paper is a study of some properties of a collection of bounded linear operators resulting from terraced matrices M acting through multiplication on <TEX>${\ell}^2$</TEX>; the term terraced matrix refers to a lower triangular infinite matrix with constant row segments. Sufficient conditions are found for M to be posinormal, meaning that <TEX>$MM^*=M^*PM$</TEX> for some positive operator P on <TEX>${\ell}^2$</TEX>; these conditions lead to new sufficient conditions for the hyponormality of M. Sufficient conditions are also found for the adjoint <TEX>$M^*$</TEX> to be posinormal, and it is observed that, unless M is essentially trivial, <TEX>$M^*$</TEX> cannot be hyponormal. A few examples are considered that exhibit special behavior.
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