Theory of operators, Part II. operator algebras

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.

Generalized Stability Theory . Part II : Nonautonomous Operators

An extension of classical stability theory to address the stability of perturbations to time-dependent systems is described. Nonnonnality is found to play a central role in determining the stability of systems �ovemed by nonautonomous operators associated with time-dependent systems. This pivotal role of nonnonnahty provIdes a conceptual bridge by which the generalized stability theory develope...

Operator Theory and Operator Algebras

0 A functional - analytic theory of vertex ( operator ) algebras , II

For a finitely-generated vertex operator algebra V of central charge c ∈ C, a locally convex topological completion HV is constructed. We construct on HV a structure of an algebra over the operad of the c 2 -th power Det c/2 of the determinant line bundle Det over the moduli space of genus-zero Riemann surfaces with ordered analytically parametrized boundary components. In particular, HV is a m...

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...