  Based on a Wold decomposition for families of partial isometries and
projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental
theorems from the case of single vertex graphs to the general case of countable
directed graphs with no sinks. We prove a Szego-type factorization theorem for
CKT families, which leads to information on the structure of the unit ball in
free semigroupoid algebras, and show that joint similarity implies joint
unitary equivalence for such families. For each graph we prove a generalization
of von Neumann's inequality which applies to row contractions of operators on
Hilbert space which are related to the graph in a natural way. This yields a
functional calculus determined by quiver algebras and free semigroupoid
algebras. We establish a generalization of Coburn's theorem for the C*-algebra
of a CKT family, and prove a universality theorem for C*-algebras generated by
these families. In both cases, the C*-algebras generated by quiver algebras
play the universal role.
