The Toeplitz algebra of a Hilbert bimodule

1998/06/18 by Neal J. Fowler, Fowler, Neal J., Iain Raeburn +1
Mathematics · #46L55 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.math/9806093

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

arxiv created 1998/06/23 · arxiv updated 2009/11/30

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_∞.

Related

• Cuntz-Krieger uniqueness theorem for crossed products by Hilbert bimodules
• On the universal property of Pimsner-Toeplitz C*-algebras and their continuous analogues
• C*-algebras associated to product systems of Hilbert bimodules
• Cuntz-Pimsner C*-algebras and crossed products by Hilbert C*-bimodules
• Iterating the Pimsner construction