We show that the dimension of Cuntz semigroup a [Formula: see text]-algebra is determined by dimensions semigroups its separable sub-[Formula: text]-algebras. This allows us to remove separability assumptions from previous results on semigroups. To obtain these results, we introduce notion approximation for abstract compatible with many properties are preserved and satisfy Löwenheim–Skolem cond...

The notion of separable (alternatively unramified, or decidable) objects and their place in a categorical theory of space have been described by Lawvere (see [9]), drawing on notions of separable from algebra and unramified from geometry. In [10], Schanuel constructed the generic separable object in an extensive category with products as an object of the free category with finite sums on the du...

A linear operator acting on a separable Hilbert space is called quasidiagonal if it is a compact perturbation of a block-diagonal operator (see [H]). This notion extends to C*-algebras in the form of a local approximation property. Quasidiagonality has important applications to the extension theory of C*-algebras. It was shown by Voiculescu [V2] that quasidiagonality is a topological invariant....

The Jiang–Su algebra Z has come to prominence in the classification program for nuclear C-algebras of late, due primarily to the fact that Elliott’s classification conjecture predicts that all simple, separable, and nuclear C-algebras with unperforated K-theory will absorb Z tensorially (i.e., will be Z-stable). There exist counterexamples which suggest that the conjecture will only hold for si...

We prove that all unital separable continuous fields of C*-algebras over [0, 1] with fibers isomorphic to the Cuntz algebra On (2 ≤ n ≤ ∞) are trivial. More generally, we show that if A is a separable, unital or stable, continuous field over [0, 1] of Kirchberg C*-algebras satisfying the UCT and having finitely generated K-theory groups, then A is isomorphic to a trivial field if and only if th...

Using a variation of the Murphy-Varopoulos Theorem, we give a new proof of the following R. J. Loy Theorem: Let A be a separable Banach ∗-algebra with center Z such that ZA has at most countable codimension, then every positive linear functional on A is continuous.

We show that the generic symmetric monoidal category with a commutative separable algebra which has a Σ-family of actions is the category of cospans of finite Σ-labelled graphs restricted to finite sets as objects, thus providing a syntax for automata on the alphabet Σ. We use this result to produce semantic functors for Σautomata.

The main result is to show that the space of nonmonotonic fuzzy measures on a measurable space (X,X) with total variation norm is separable if and only if the -algebra X is a finite set. Our result is related to fuzzy analysis, functional spaces and discrete mathematics. © 2007 Elsevier B.V. All rights reserved.

On a separable C-algebra A every (completely) bounded map which preserves closed two sided ideals can be approximated uniformly by elementary operators if and only if A is a finite direct sum of C-algebras of continuous sections vanishing at ∞ of locally trivial C-bundles of finite type.

The Connes Embedding Problem (CEP) asks whether every separable II1 factor embeds into an ultrapower of the hyperfinite II1 factor. We show that the CEP is equivalent to the computability of the universal theory of every type II1 von Neumann algebra. We also derive some further computability-theoretic consequences of the CEP.