The Toeplitz algebra of a Hilbert bimodule

Suppose a C*-algebra A acts by adjointable operators on a Hilbert A-module X. Pimsner constructed a C*-algebra O-x which includes, for particular choi ces of X, crossed products of A by Z, the Cuntz algebras O-n, and the Cuntz -Krieger algebras O-B. Here we analyse the representations of the correspon ding Toeplitz algebra. One consequence is a uniqueness theorem for the Toep litz-Cuntz-Krieger algebras of directed graphs, which includes Cuntz's uniq ueness theorem for O-infinity.