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The Toeplitz Algebra Of A Hilbert Bimodule, Neal J. Fowler, Iain Raeburn

Faculty of Engineering and Information Sciences - Papers: Part A

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 _∞.