The bicommutant theorem is a theorem within the field of functional analysis regarding certain topological properties of function algebras. The theorem says that, given a Hilbert space , a -subalgebra of which acts nondegenerately is dense in its bicommutant under the so-called sigma-strong operator topology. Here, denotes the algebra of bounded operators from to itself.
The Bicommutant theorem is generally attributed to John von Neumann.
The theorem itself has a number of important corollaries, not the least among which is an equivalence by which one can classify a subalgebra of as a von Neumann Algebra.