The Toeplitz algebra of a Hilbert bimodule
Abstract
Suppose a C*-algebra A acts by adjointable operators on a Hilbert A-module X. Pimsner constructed a C*-algebra OX which includes, for particular choices of X, crossed products of A by Z, the Cuntz algebras On, and the Cuntz-Krieger algebras OB. 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∞.
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