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

Let $A$ be a unital $C^*$-algebra and $X$ an invulutive $A-A$-equivalence bimodule. Let $A\subset C_X$ be the unital inclusion of unital $C^*$-algebras induced by $X$. We suppose that $A' \cap C_X =\mathbf{C} 1$. We shall compute the Picard…

We study conditional expectations generated by an abelian $ C^* $-subalgebra in the centralizer of a positive functional. We formulate and prove Jensen's inequality for functions of several variables with respect to this type of conditional…

We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and…

For a conditional expectation E on a (unital) C*-algebra A there exists a real number K>=1 such that the mapping (K.E-id_A) is positive if and only if there exists a real number L>=1 such that the mapping (L.E-id_A) is completely positive,…

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 into the injective envelope I(D) of D whose…

Motivated by advances in categorical probability, we introduce non-commutative almost everywhere (a.e.) equivalence and disintegrations in the setting of C*-algebras. We show that C*-algebras (resp. W*-algebras) and a.e. equivalence classes…

When $\mathcal D$ is strongly self-absorbing we say an inclusion $B \subseteq A$ is $\mathcal D$-stable if it is isomorphic to the inclusion $B \otimes \mathcal D \subseteq A \otimes \mathcal D$. We give ultrapower characterizations and…

In an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital $C^*$-algebras, with a particular focus on gapped maps for…

We derive faithful inclusions of C*-algebras from a coend-type construction in unitary tensor categories. This gives rise to different potential notions of discreteness for an inclusion in the non-irreducible case, and provides a unified…

We show that every interaction group extending an action of an Ore semigroup by injective unital endomorphisms of a C*-algebra, admits a dilation to an action of the corresponding enveloping group on another unital C*-algebra, of which the…

We characterize exotic C*-algebras of twisted, principal \'etale groupoids, together with the abelian subalgebra associated to the unit space, as precisely being the inclusions "$A\subseteq B$" of C*-algebras in which $A$ is abelian,…

Order unit property of a positive element in a $C^{*}$-algebra is defined. It is proved that precisely projections satisfy this order theoretic property. This way, unital hereditary $C^{*}$-subalgebras of a $C^{*}$-algebra are…

We study the problem of extending a state on an abelian $C^*$- subalgebra to a tracial state on the ambient $C^*$-algebra. We propose an approach that is well-suited to the case of regular inclusions, in which there is a large supply of…

We characterize the canonical diagonal subalgebra of the C*-algebra associated with a generalized Boolean dynamical system. We also introduce a particular commutative subalgebra, which we call the abelian core, in our C*-algebra. We then…

The class of abelian $p$-groups are an example of some very interesting phenomena in computable structure theory. We will give an elementary first-order theory $T_p$ whose models are each bi-interpretable with the disjoint union of an…

Examples of simple, separable, unital, purely infinite $C^*$--algebras are constructed, including: (1) some that are not approximately divisible; (2) those that arise as crossed products of any of a certain class of $C^*$--algebras by any…

Let B be a unital C*-algebra, let A be a unital subalgebra, and let E be a conditional expectation from B to A with index-finite type and a quasi-basis of n elements. Then the topological stable rank satisfies \tsr (B) \leq \tsr (A) + n -…

We study regular irreducible inclusions $B\subset A$ of simple unital $C^*$-algebras admitting a conditional expectation. We introduce a generalized notion of quasi-basis extending Watatani's framework and show that such inclusions admit a…

We characterise Exel's noncommutative Cartan subalgebras in several ways using uniqueness of conditional expectations, relative commutants, or purely outer inverse semigroup actions. We describe in which sense the crossed product…

We introduce the notion of a Cartan envelope for a regular inclusion (C,D). When a Cartan envelope exists, it is the unique, minimal Cartan pair into which (C,D) regularly embeds. We prove a Cartan envelope exists if and only if (C,D) has…