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

Takeshi Katsura

Vol. 230 (2007), No. 1, 107–145

DOI: 10.2140/pjm.2007.230.107

Abstract

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.

Keywords

C^∗-algebra, C^∗-correspondence, Hilbert module, Cuntz–Pimsner algebras, ideal structure, crossed products

Mathematical Subject Classification 2000

Primary: 46L05, 46L55

Milestones

Received: 25 October 2003

Accepted: 8 December 2006

Published: 1 March 2007