Finite von Neumann algebra
In other words, for an operator V in a finite von Neumann algebra ifdenote a finite von Neumann algebra with centerOne of the fundamental characterizing properties of finite von Neumann algebras is the existence of a center-valued trace.is finite if and only if there exists a normal positive bounded mapA von Neumann algebra N is called a factor if Z(N) is one-dimensional, that is, Z(N) consists of multiples of the identity I. Theorem Every finite-dimensional von Neumann algebra M is a direct sum of m factors, where m is the dimension of Z(M).The above is a special case of the central decomposition of von Neumann algebras.