Model theory of operator algebras I: stability

Model Theory of Operator Algebras Ii: Model Theory

We introduce a version of logic for metric structures suitable for applications to C*-algebras and tracial von Neumann algebras. We also prove a purely model-theoretic result to the effect that the theory of a separable metric structure is stable if and only if all of its ultrapowers associated with nonprincipal ultrafilters on N are isomorphic even when the Continuum Hypothesis fails.

Operator Theory and Operator Algebras

Multiplicity Theory for Operator Algebras.

I Since (3.1) is homogeneous of degree zero in vm, vm, and am in (3.2) can be taken to be dym/dy4, d2y/(dy4)2,resp. Thenv4 = 1 a4= 0 10 On the nullspheres (X = 0) one gets If = 0, where R = 0-i.e., just the Coulomb infinity. 11 E.g., X acts like a sort of gauge, or numerical length assigned to some standard physical rod by the observer at xm. This rod can be assigned any positive value, but not...

On the Homology Theory of Operator Algebras

For given Banach algebras A and B, we define a free resolution of algebraB over a homomorphism f : A → B and study some properties of the relative cyclic homology.

The Algebraic K-theory of Operator Algebras

We the study the algebraic K-theory of C∗-algebras, forgetting the topology. The main results include a proof that commutative C∗-algebras are K-regular in all degrees (that is, all their NKi-groups vanish) and extensions of the Fischer-Prasolov Theorem comparing algebraic and topological K-theory with finite coefficients.