Related papers: Ideals in Cross Sectional C*-algebras of Fell Bund…

We investigate structural properties of the reduced cross-sectional algebra $C^*_r(\mathcal{B})$ of a Fell bundle $\mathcal{B}$ over a discrete group $G$. Conditions allowing one to determine the ideal structure of $C^*_r(\mathcal{B})$ are…

We construct a weak conditional expectation from the section C*-algebra of a Fell bundle over a unital inverse semigroup to its unit fibre. We use this to define the reduced C*-algebra of the Fell bundle. We study when the reduced…

We show that if $p:\B\to G$ is a Fell bundle over a locally compact groupoid $G$ and that $A=\Gamma_{0}(G^{(0)};\B)$ is the \cs-algebra sitting over $G^{(0)}$, then there is a continuous $G$-action on $\Prim A$ that reduces to the usual…

We extend the theory of tensor products of C*-algebras to the larger category of Fell bundles over locally compact groups. We prove that, like in the case of C*-algebras, there exist maximal and minimal tensor products. Given two Fell…

We study the $C^*$-algebras associated to upper-semicontinuous Fell bundles over second-countable Hausdorff groupoids. Based on ideas going back to the Packer--Raeburn "Stabilization Trick," we construct from each such bundle a groupoid…

We show that the existence of a continuous conditional expectation from a Fell bundle to a Fell subbundle implies that the full cross-sectional C*-algebra of the subbundle is contained in the full cross-sectional C*-algebra of the bundle,…

This is a book about Partial Actions and Fell Bundles with applications to C*-algebras generated by partial isometries. Here is the table of contents: 1-Introduction, 2-Partial actions, 3-Restriction and globalization, 4-Inverse semigroups,…

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…

We characterize the ideal of continuous-trace elements in a separable transformation-group $C^{*}$-algebra $C_0(X)\times G$. In addition, we identify the largest Fell ideal, the largest liminal ideal and the largest postliminal ideal.

Given a C*-algebra B which is graded over a discrete group G we consider ideals of B which are invariant under the projections onto each of the grading subspaces. If G is exact and the standard conditional expectation of B is faithful we…

We introduce and study actions of Fell bundles over discrete groups on Hilbert bundles. Many examples of such actions are presented. We discuss the connection with positive definite bundle maps between Fell bundles, culminating in the…

We define possibly unsaturated, upper semicontinuous Fell bundles over Hausdorff, locally compact groupoids and establish a universal property for representations of their full section C*-algebras on Hilbert modules over arbitrary…

In this paper we give a simple proof of the maximality of dual coactions on full cross-sectional C*-algebras of Fell bundles over locally compact groups. As applications we extend certain exotic crossed-product functors in the sense of…

Given a Fell bundle $\mathcal{B}=\{B_t\}_{t\in G}$ over a locally compact and Hausdorff group $G$ and a closed subgroup $H\subset G,$ we construct quotients $C^*_{H\uparrow \mathcal{B}}(\mathcal{B})$ and $C^*_{H\uparrow G}(\mathcal{B})$ of…

A C*-dynamical system is said to have the ideal separation property if every ideal in the corresponding crossed product arises from an invariant ideal in the C*-algebra. In this paper we characterize this property for unital C*-dynamical…

We define partial product systems over N. They generalise product systems over N and Fell bundles over Z. We define Toeplitz C*-algebras and relative Cuntz-Pimsner algebras for them and show that the section C*-algebra of a Fell bundle over…

Let G be a locally compact Abelian group. Following Ruy Exel, we view Fell bundles over the Pontrjagin dual of G as continuous spectral decompositions of G-actions on C*-algebras. We classify such spectral decompositions using certain dense…

We give a notion of equivalence for Fell bundles over groups, not necessarily saturated nor separable, and show that equivalent Fell bundles have Morita-Rieffel equivalent cross-sectional $C^*$-algebras. Our notion is originated in the…

We introduce a natural concept of positive definiteness for bundle maps between Fell bundles over (possibly different) discrete groups and describe several examples. Such maps induce completely positive maps between the associated full…

We show that every Fell bundle B over a locally compact group G is "proper" in a sense recently introduced by Ng. Combining our results with those of Ng we show that if B satisfies the "approximation property" then it is amenable in the…