The Toeplitz algebra of a Hilbert bimodule

Details The Toeplitz algebra of a Hilbert bimodule The Toeplitz algebra of a Hilbert bimodule

1998-06-18

arxiv.org/abs/math/9806093v3

Mathematics

Operator Algebras

AMS-LaTeX, 22 pages; originally posted an old version by mistake

Scientific paper

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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