Operator Algebras

An operator algebra is a self-adjoint subalgebra of the algebra of bounded operators on a Hilbert space which is closed in a specific topology.

The theory of operator algebras was initiated for applications in the operator theory, the theory of unitary group representations, the mathematical formulations of quantum mechanics and abstract algebras. Nowadays, the theory of operator algebras are related to many areas of mathematics and physics.

Operator algebras can be classified into von Neumann algebras and C*-algebras. I mainly study C*-algebras. In particular, I am interested in the structures of stably projectionless C*-algebras recently.