The Toeplitz algebra of a Hilbert bimodule

Authors

Neal J. Fowler, University of Newcastle
Iain Raeburn, University of WollongongFollow

RIS ID

18730

Publication Details

Fowler, N. J. & Raeburn, I. (1999). The Toeplitz algebra of a Hilbert bimodule. Indiana University Mathematics Journal, 48 (1), 155-181.

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 CuntzKrieger algebras 𝒪 _B. Here we analyse the representations of the corresponding Toeplitz algebra. One consequence is a uniqueness theorem for the ToeplitzCuntz-Krieger algebras of directed graphs, which includes Cuntz’s uniqueness theorem for 𝒪 _∞.