Suppose A is a separable unital C(X)-algebra each fibre of which is isomorphic to the same strongly self-absorbing and K1-injective C∗-algebra D. We show that A and C(X) ⊗ D are isomorphic as C(X)-algebras provided the compact Hausdorff space X is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.

1991 Abstract. A topological space X is called A-real compact, if every algebra homomorphism from A to the reals is an evaluation at some point of X, where A is an algebra of continuous functions. Our main interest lies on algebras of smooth functions. In AdR] it was shown that any separable Banach space is smoothly real compact. Here we generalize this result to a huge class of locally convex ...

We give an example of a simple separable C*-algebra which is not isomorphic to its opposite algebra. Our example is nonnuclear and stably finite, has real rank zero and stable rank one, and has a unique tracial state. It has trivial K1, and its K0-group is order isomorphic to a countable subgroup of R.

The C*-algebra of bounded operators on the separable Hilbert space cannot be mapped to a W*-algebra in such a way that each unital commutative C*-subalgebra C(X) factors normally through `∞(X). Consequently, there is no faithful functor discretizing C*-algebras to W*-algebras this way.

This work introduces the concept of an M-complete approximate identity (M-cai) for a given operator subspace X of an operator space Y. M-cai's generalize central approximate identities in ideals in C *-algebras, for it is proved that if X admits an M-cai in Y , then X is a complete M-ideal in Y. It is proved, using " special " M-cai's, that if J is a nuclear ideal in a C *-algebra A, then J is ...

We have measured how color appearance of squarewave bars varies with stimulus strength and spatial frequency. Observer's adjusted the color of an uniform patch to match the color appearance of the bars in squarewave patterns. We used low to moderate squarewave patterns, from one to eight cycles per degree (cpd). The matches are not photoreceptor matches, but rather are established at more centr...

Abstract We compute the generator rank of a subhomogeneous $C^*\!$ -algebra in terms covering dimension pieces its primitive ideal space corresponding to irreducible representations fixed dimension. deduce that every $\mathcal {Z}$ -stable approximately algebra has one, which means generic element such an is generator. This leads strong solution problem for classifiable, simple, nuclear -algebr...

Let M⊂B(H) be a von Neumann algebra acting on the (separable) Hilbert space H. We first prove that M is finite if and only if, for every x∈M all vectors ξ,η∈H, coefficient function u↦⟨uxu∗ξ|η⟩ weakly almost periodic topological group UM of unitaries in (equipped with weak operator topology). The main device unique invariant mean C∗-algebra WAP(UM) functions UM. Next, we direct sum diffuse, abel...

We initiate the large scale geometric study of Banach-Lie groups, especially linear groups. show that exponential length, originally introduced by Ringrose for unitary groups $C^*$-algebras, defines quasi-isometry type any connected group. As an illustrative example, we consider separable abelian unital $C^*$-algebras with spectrum having finitely many components, which classify up to topologic...

Kadison and Kastler introduced a natural metric on the collection of all C∗-subalgebras of the bounded operators on a separable Hilbert space. They conjectured that sufficiently close algebras are unitarily conjugate. We establish this conjecture when one algebra is separable and nuclear. We also consider one-sided versions of these notions, obtaining embeddings from certain near inclusions inv...