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The Toeplitz Algebra Of A Hilbert Bimodule, Neal J. Fowler, Iain Raeburn
The Toeplitz Algebra Of A Hilbert Bimodule, Neal J. Fowler, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
Suppose a C โ -algebra A acts by adjointable operators on a Hilbert A -module X. Pimsner constructed a C โ -algebra ๐ช X which includes, for particular choices of X , crossed products of A by Z , the Cuntz algebras ๐ช n , and the CuntzKrieger algebras ๐ช 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 Cuntzโs uniqueness theorem for ๐ช โ.