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The Toeplitz algebra of a Hilbert bimodule

Neal J. Fowler·Iain Raeburn
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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 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_\infty.

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Neal J. Fowler, Iain Raeburn. 1998-06-23. The Toeplitz algebra of a Hilbert bimodule. https://arxiv.org/abs/math/9806093

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