Abstract: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 choices of X, crossed products of A by Z, the Cuntz ...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 choices 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 corresponding Toeplitz algebra.One consequence is a uniqueness theorem for the Toeplitz-Cuntz-Krieger algebras of directed graphs, which includes Cuntz's uniqueness theorem for O ∞ .Read More