Let A be a simple separable unital locally approximately subhomogeneous C*algebra (locally ASH algebra). It is shown that A ⊗ Q can be tracially approximated by unital Elliott-Thomsen algebras with trivial K1-group, where Q is the universal UHF algebra. In particular, it follows that A is classifiable by the Elliott invariant if A is Jiang-Su stable.

Jiang and Su and (independently) Elliott discovered a simple, nuclear, infinite-dimensional C-algebra Z having the same Elliott invariant as the complex numbers. For a nuclear C-algebra A with weakly unperforated K∗-group the Elliott invariant of A ⊗ Z is isomorphic to that of A. Thus, any simple nuclear C-algebra A having a weakly unperforated K∗-group which does not absorb Z provides a counte...

We say that a C∗-algebra X has the approximate n-th root property (n ≥ 2) if for every a ∈ X with ‖a‖ ≤ 1 and every ε > 0 there exits b ∈ X such that ‖b‖ ≤ 1 and ‖a − bn‖ < ε. Some properties of commutative and non-commutative C∗-algebras having the approximate nth root property are investigated. In particular, it is shown that there exists a non-commutative (resp., commutative) separable unita...

We show that the (co)endomorphism algebra of a sufficiently separable “fibre” functor into Vectk, for k a field of characteristic 0, has the structure of what we call a “unital” von Neumann core in Vectk. For Vectk, this particular notion of algebra is weaker than that of a Hopf algebra, although the corresponding concept in Set is again that of a group.

We investigate strictly positive finitely additive measures on Boolean algebras and strictly positive Radon measures on compact zerodimensional spaces. The motivation is to find a combinatorial characterisation of Boolean algebras which carry a strictly positive finitely additive finite measure with some additional properties, such as separability or nonatomicity. A possible consistent characte...

Assuming the continuum hypothesis, we show that the Calkin algebra has 2 ℵ 1 outer automorphisms. Let H be a separable infinite dimensional Hilbert space, let L(H) be the algebra of bounded operators on H, let K(H) be the algebra of compact operators on H, and let Q = L(H)/K(H) be the Calkin algebra. A long-standing problem asks whether every automorphism of Q is inner, that is, of the form x →...

I show that each étale n-cohomology class on noetherian schemes comes from a Čech cocycle, provided that any n-tuple of points admits an affine open neighborhood. Together with results of Raeburn and Taylor on the bigger Brauer group, this implies that for schemes such that each pair of points admits an affine open neighborhood, any étale Gm-gerbe comes from a coherent central separable algebra...