Ideal structure of C∗-algebras associated with C∗-correspondences

By Takeshi Katsura. 2003

96 citations recorded by the source corpus.

We study the ideal structure of C*-algebras arising from C*-correspondences. We prove that gauge-invariant ideals of our C*-algebras are parameterized by certain pairs of ideals of original C*-algebras. We show that our C*-algebras have a nice property that should be possessed by a generalization of crossed products. Applications to crossed products by Hilbert C*-bimodules and relative Cuntz?Pimsner algebras are also discussed.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6780b8de62f6cb83a00a321efabdf5a784f9ca36

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In Applied Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Adding tails to $C^*$-correspondences (2002, methodology): “t ˜τ is injective. Hence ˜τ|S = τ = κ◦ρ is injective, and ρ is injective. To conclude this section we shall interpret our result in the relative CuntzPimsner setting. Remark 5.4. Katsura has shown in [12] that if O(K,X) is a relative Cuntz-Pimsner algebra, then there exists a C∗-correspondence X′ wi”
On C -algebras associated with C -correspondences (2003, methodology): “The idea of the proof can be seen in [ Ka1 , Section 4] (and also in [P, Section 3], [FMR, Section 4]).”
Co‐universal algebras associated to product systems, and gauge‐invariant uniqueness theorems (2009, background): “In an impressive array of papers [21, 22, 23] Katsura, drawing on insight from graph algebras and drawing on results on quotients of Cuntz-Pimsner algebras developed in [19], not only expanded Pimsner’s theory of C∗-algebras associated with Hilbert bimodules beyond the case of isometric left actions”