Von Neumann Algebra

A von Neumann algebra (W*-algebra) is a *‑subalgebra of B(H), the bounded operators on a Hilbert space H, that contains the identity and is closed in the weak (or strong) operator topology; equivalently, by the bicommutant theorem, it is equal to its bicommutant. Von Neumann algebras often carry a predual and admit rich projection lattices.