Matrix construction of subnormal tuples of finite type ✩

We review Xia’s analytic model for subnormal tuples of operators as well as a matricial decomposition of pure subnormal tuples of Eschmeier and Putinar. Based on these developments we create a matricial construction of pure subnormal tuples of finite type from the Xia unitary invariants. In the process we develop necessary and sufficient conditions for sets of operators {C j0, D j1 } to be the Xia invariants of a subnormal tuple.  2003 Elsevier Inc. All rights reserved.