Induced representations of C∗-algebras

Continuous-trace groupoid 𝐶*-algebras. III

“…The next result is standard; see for example, Rieffel's Theorem 5.9 (Induction in Stages) and Proposition 6.26 in [17]. We omit the proof.…”

“…which is essentially a generalized conditional expectation in the sense of Rieffel [17,Definition 4.12]. Unfortunately we cannot use Rieffel's definition directly as C c (A) acts on the right of C c (G u ) rather than C c (G), and the former is not an algebra.…”

A stabilization theorem for Fell bundles over groupoids

“…We assume that our Fell bundles are second countable and saturated and they have enough sections (in the sense that evaluation of continuous sections at g is surjective onto B(g) for each g [28, p. 16]). Since B(g) is an A(r(g))-A(s(g)) imprimitivity bimodule, the Rieffel correspondence [33,38,39] induces a homeomorphism h g : Prim A(s(g)) → Prim A(r(g)).…”

An Introduction to Noncommutative Spaces and their Geometries

“…Hilbert modules have been (and are) used in a variety of applications, notably for the notion of strong Morita equivalence. The subject started with the works [87] and [84]. We refer to [102] for a very nice introduction while we report on the fundamentals of the theory.…”

“…In this Appendix, we describe the notion of strong Morita equivalence [87,88] between two C * -algebras. This really boils down to an equivalence between the corresponding representation theories.…”