From Operator Algebras to Complexity Theory and Back

Operator Theory and Operator Algebras

K-theory associated to vertex operator algebras

We introduce two K-theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algebras. We verify the cohomological properties of these K-theories, and construct a natural homomorphism from the VOA K-theory to the associative algebra K-theory.

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...

Recent Advances in Operator Theory and Operator Algebras

In this article the spectral theorem for right linear compact normal operators on quaternionic Hilbert spaces is proved. Though the version of spectral theorem for such operators in quaternionic Hilbert space is appeared in recent literature using the left multiplication and considering the Hilbert space to be slice complex linear, we present a different approach, which is similar to the classi...

Elements of Operator Algebras and Modular Theory