Intermediate C*-algebras of Cartan embeddings

  title={Intermediate C*-algebras of Cartan embeddings},
  author={Jonathan Henry Brown and Ruy Exel and Adam Hanley Fuller and David R. Pitts and Sarah Reznikoff},
  journal={Proceedings of the American Mathematical Society, Series B},
<p>Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="" alttext="upper A"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding="application/x-tex">A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a C<inline-formula content-type="math/mathml"> <mml:math xmlns:mml="" alttext="Superscript asterisk"> <mml:semantics> <mml:msup> <mml:mi /> <mml:mo… 
Irreducible inclusions of simple C$^*$-algebras
The literature contains interesting examples of inclusions of simple C∗-algebras with the property that all intermediate C∗-algebras likewise are simple. In this article we take up a systematic study
A uniqueness theorem for twisted groupoid C*-algebras
Exotic Ideals in Represented Free Transformation Groups
Let Γ be a discrete group freely acting via homeomorphisms on the compact Hausdorff space X and let C(X)⋊η Γ be the completion of the convolution algebra Cc(Γ, C(X)) with respect to a C-norm η. A
Normalizers and Approximate Units for Inclusions of C*-Algebras
. For an inclusion of C ∗ -algebras D ⊆ A with D abelian, we show that when n ∈ A normalizes D , n ∗ n and nn ∗ commute with D . As a corollary, when D is a regular MASA in A , every approximate unit
Certain submodules in groupoid C*-algebras and discrete group coactions on groupoid C*-algebras
. In this paper, we investigate certain submodules in C*-algebras associated to effective ´etale groupoids. First, we show that a submodule generated by normalizers is a closure of the set of
O A ] 2 5 M ay 2 02 1 Irreducible inclusions of simple C ∗-algebras
The literature contains interesting examples of inclusions of simple C∗-algebras with the property that all intermediate C∗-algebras likewise are simple. In this article we take up a systematic study
A correspondence between inverse subsemigroups, open wide subgroupoids and Cartan intermediate C*-subalgebras
For a given inverse semigroup action on a topological space, one can associate an etale groupoid. We prove that there exists a correspondence between the certain subsemigroups and the open wide


C*-Algebras and Finite-Dimensional Approximations
Fundamental facts Basic theory: Nuclear and exact $\textrm{C}^*$-algebras: Definitions, basic facts and examples Tensor products Constructions Exact groups and related topics Amenable traces and
Cartan Subalgebras in C*-Algebras of Haus dorff étale Groupoids
The reduced C*-algebra of the interior of the isotropy in any Hausdorff étale groupoid G embeds as a C*-subalgebra M of the reduced C*-algebra of G. We prove that the set of pure states of M with
Bimodules over Cartan MASAs in von Neumann Algebras, Norming Algebras, and Mercer's Theorem
In a 1991 paper, R. Mercer asserted that a Cartan bimodule isomorphism between Cartan bimodule algebras A_1 and A_2 extends uniquely to a normal *-isomorphism of the von Neumann algebras generated by
Theory of operator algebras
I Fundamentals of Banach Algebras and C*-Algebras.- 0. Introduction.- 1. Banach Algebras.- 2. Spectrum and Functional Calculus.- 3. Gelfand Representation of Abelian Banach Algebras.- 4. Spectrum and
For a Banach D-bimodule M over an abelian unital C -algebraD, we define E 1 (M) as the collection of norm-one eigenvectors for the dual action of D on the Banach space dual M # . Equip E 1 (M) with
Amenability for Fell bundles.
Given a Fell bundle $\B$, over a discrete group $\Gamma$, we construct its reduced cross sectional algebra $C^*_r(\B)$, in analogy with the reduced crossed products defined for C*-dynamical systems.
Inclusions of simple $C^*$-algebras
We prove that if a conditional expectation from a simple $C^*$-algebra onto its $C^*$-subalgebra satisfies the Pimsner-Popa inequality, there exists a quasi-basis. As an application, we establish the
We study pairs (C,D) of unital C*-algebras where D is a regular abelian C*-subalgebra of C. When D is a MASA in C, we prove the existence and uniqueness of a completely positive unital map E of C
Graded C*-algebras and twisted groupoid C*-algebras
Let $C^*$-algebra that is acted upon by a compact abelian group. We show that if the fixed-point algebra of the action contains a Cartan subalgebra $D$ satisfying an appropriate regularity condition,
Amenable actions of discrete groups
We study amenable actions on graphs having infinitely many ends, giving a generalized answer to Ceccherini’s question on groups with infinitely many ends. A.1 Statement of the result An action of a