讲座内容：

Let M be a separable von Neumann algebra with center Z(M). An operator T in M is called irreducible if W*(T)'\cap M=Z(M). In this talk, we present three theorems: (1) The set of irreducible operators in M is norm-dense; (2) every operator in M is the sum of two irreducible operators; (3) every nonzero operator in M is the product of two irreducible operators if M is a factor.