Toeplitz Algebras of Correspondences and Endomorphisms of Sums of Type I Factors

It is a well-known fact that endomorphisms of B(H) are intimately connected with families of mutually orthogonal isometries, that is, with representations of the so-called Toeplitz C*-algebras. In this paper we consider a natural generalization of this connection between the representation theory of certain C*-algebras associated with graphs and endomorphisms of certain von Neumann subalgebras of (H). Our primary results give criteria by which it may be determined if two representations give rise to equal or conjugate endomorphisms.