Topological freeness for C*-correspondences
Journal article, Peer reviewed
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Date
2019Metadata
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- Institutt for matematiske fag [2531]
- Publikasjoner fra CRIStin - NTNU [38525]
Original version
Journal of Mathematical Analysis and Applications. 2019, 473 (2), 749-785. 10.1016/j.jmaa.2018.12.069Abstract
We study conditions that ensure uniqueness theorems of Cuntz–Krieger type for relative Cuntz–Pimsner algebras associated to a ⁎-correspondence X over a ⁎-algebra A. We give general sufficient conditions phrased in terms of a multivalued map acting on the spectrum of A. When is of Type I we construct a directed graph dual to X and prove a uniqueness theorem using this graph. When is liminal, we show that topological freeness of this graph is equivalent to the uniqueness property for , as well as to an algebraic condition which we call J-acyclicity of X. As an application we improve the Fowler–Raeburn uniqueness theorem for the Toeplitz algebra . We give new simplicity criteria for . We generalize and enhance uniqueness results for relative quiver ⁎-algebras of Muhly and Tomforde. We also discuss applications to crossed products by endomorphisms.