Operator Algebras Over C*-Correspondences

  • Baruch Solel
Chapter
Part of the NATO ASI Series book series (ASIC, volume 495)

Abstract

Our aim in this paper is to describe the construction of Cuntz-Pimsner C*-algebras and a class of distinguished, nonselfadjoint, subal-gebras of these C*-algebras, called tensor algebras. We shall discuss the representations of these algebras and present some results and examples. In section 1 we present sufficient conditions for the simplicity of Cuntz-Pimsner algebras and in section 2 we discuss dilations and extensions of representations of the tensor algebras leading to the identification of their C*-envelopes. Most of the results (with proofs) can be found in the work of Pimsner [26] and in a joint work with P. Muhly [21] and [22]

Keywords

Hilbert Space Direct Summand Operator Algebra Toeplitz Operator Contractive Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Baruch Solel
    • 1
  1. 1.Department of MathematicsTechnion—Israel Institute of TechnologyHaifaIsrael

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