Essentially commutative C*-algebras with essential spectrum homeomorphic to S2n−1

The Classification of Separable Simple C*-algebras Which Are Inductive Limits of Continuous-trace C*-algebras with Spectrum Homeomorphic to the Closed Interval [0,1]

A classification is given of certain separable nuclear C*algebras not necessarily of real rank zero, namely, the class of separable simple C*-algebras which are inductive limits of continuoustrace C*-algebras whose building blocks have spectrum homeomorphic to the closed interval [0, 1], or to a disjoint union of copies of this space. Also, the range of the invariant is calculated. 1991 Mathema...

Commutative C ∗-algebras and Σ-normal Morphisms

We prove in an elementary fashion that the image of a commutative monotone σ-complete C-algebra under a σ-normal morphism is again monotone σ-complete and give an application of this result in spectral theory.

Non-Commutative Dimension for C*-Algebras

Commutative C-algebras and Sequentially Normal Morphisms

We show that the image of a commutative monotone sequentially complete C∗-algebra, under a sequentially normal morphism, is again a monotone sequentially complete C-algebra, and also a monotone sequentially closed C∗-subalgebra. As a consequence, the image of an algebra of this type, under a sequentially normal representation in a separable Hilbert space, is strongly closed. In the case of a un...

From Kleisli Categories to Commutative C *-Algebras: Probabilistic Gelfand Duality

C -algebras form rather general and rich mathematical structures that can be studied with different morphisms (preserving multiplication, or not), and with different properties (commutative, or not). These various options can be used to incorporate various styles of computation (set-theoretic, probabilistic, quantum) inside categories of C -algebras. At first, this paper concentrates on the com...