Universal operator algebras associated to contractive sequences of non-commuting operators

We characterize the minimal isometric dilation of a non-commutative contractive sequence of operators as a universal object for certain diagrams of completely positive maps. A non-spatial construction of the minimal isometric dilation is also given, using Hilbert modules over C*-algebras. It is shown that the non-commutative disc algebras A(n) (n greater than or equal to 2) are the universal algebras generated by contractive sequences of operators and the identity, and C*(S-1,...,S-n) (n greater than or equal to 2), the extension through compact operators of the Cuntz algebra O-n, is the universal C*-algebra generated by a contractive sequence of isometries. It is also shown that the algebras A(n) and C*(S-1,...,S-n) are completely isometrically isomorphic to some free operator algebras considered by D. Blecher. In particular, the universal operator algebra of a row (respectively column) contraction is identified with a subalgebra of C*(S-1,...,S-n). The internal characterization of the matrix norm on a universal algebra leads to some factorization theorems.