Related papers: Unique conditional expectations for abelian $C^*$-…

Let $G$ be a discrete group acting on a unital $C^*$-algebra $\mathcal{A}$ by $*$-automorphisms. We characterize (in terms of the dynamics) when the inclusion $\mathcal{A} \subseteq \mathcal{A} \rtimes_r G$ has a unique conditional…

Given an inclusion D $\subseteq$ C of unital C*-algebras, a unital completely positive linear map $\Phi$ of C into the injective envelope I(D) of D which extends the inclusion of D into I(D) is a pseudo-expectation. The set PsExp(C,D) of…

We determine when there is a unique conditional expectation from a semifinite von Neumann algebra onto a singly-generated maximal abelian *-subalgebra. Our work extends the results of Kadison and Singer via new methods, notably the…

We prove implications among the conditions in the title for an inclusion of a C*-algebra A in a C*-algebra B, and we also relate this to several other properties in case B is a crossed product for an action of a group, inverse semigroup or…

The $C^*$-inclusion $\mathcal{A} \subseteq \mathcal{B}$ is said to be hereditarily essential if for every intermediate $C^*$-algebra $\mathcal{A} \subseteq \mathcal{C} \subseteq \mathcal{B}$ and every non-zero ideal $\{0\} \neq \mathcal{J}…

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,…

We shall introduce the notions of the strong Morita equivalence for unital inclusions of unital $C^*$-algebras and conditional expectations from an equivalence bimodule onto its closed subspace with respect to conditional expectations from…

We introduce the category of C*-discrete inclusions of C*-algebras $A\subset B$ with a faithful conditional expectation $E:B\twoheadrightarrow A$. This class includes many examples such as finite Watatani index inclusions, and also abundant…

Let $j:Y \to X$ be a continuous surjection of compact metric spaces. Whyburn proved that $j$ is irreducible, meaning that $j(F) \subsetneq X$ for any proper closed subset $F \subsetneq Y$, if and only if $j$ is almost one-to-one, in the…

Let $P \subset A$ be a inclusion of unital C*-algebras and $E\colon A \to P$ be a conditional expectation of index finite type. We introduce a Rokhlin property for $E$ and discuss about $\mathcal{D}$-absorbing proeprty, where $\mathcal{D}$…

Let $P \subset A$ be an inclusion of $\sigma$-unital C*-algebras with a finite index in the sense of Izumi. Then we introduce the Rokhlin property for a conditional expectation $E$ from $A$ onto $P$ and show that if $A$ is simple and…

Let $\mathcal{N}\subset\mathcal{M}$ be a unital inclusion of arbitrary von Neumann algebras. We give a 2-{$C^*$}-categorical/planar algebraic description of normal faithful conditional expectations…

Let $G \curvearrowright A$ be an action of a discrete group on a unital $C^*$-algebra by $*$-automorphisms. In this note, we give two sufficient dynamical conditions for the $C^*$-inclusion $A \subseteq A \rtimes_r G$ to be norming in the…

We prove that an inclusion $\mathcal{B} \subset \mathcal{A}$ of simple unital $C^*$-algebras with a finite-index conditional expectation is regular if and only if there exists a finite group $G$ that admits a cocycle action…

We study uniform perturbations of crossed product C$^*$-algebras by amenable groups. Given a unital inclusion of C$^*$-algebras $C\subseteq D$ and sufficiently close separable intermediate C$^*$-subalgebras $A$, $B$ for this inclusion with…

The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([Ph88]) and Ando-Kirchberg ([AK14]). In this paper we give a complete answer to their question: A separable C*-algebra…

We examine a certain type of abelian C*-subalgebras that allow one to give a unified treatment of two uniqueness theorems: for graph C*-algebras and for certain reduced crossed products.

Let $A$ be a C$^*$-algebra and let $D$ be a Cartan subalgebra of $A$. We study the following question: if $B$ is a C$^*$-algebra such that $D \subseteq B \subseteq A$, is $D$ a Cartan subalgebra of $B$? We give a positive answer in two…

We shall introduce the notion of the Picard group for an inclusion of $C^*$-algebras. We shall also study its basic properties and the relation between the Picard group for an inclusion of $C^*$-algebras and the ordinary Picard group.…

We investigate recent uniqueness theorems for reduced $C^*$-algebras of Hausdorff \'{e}tale groupoids in the context of inverse semigroups. In many cases the distinguished subalgebra is closely related to the structure of the inverse…