The bicommutant theorem is a theorem within the field of functional analysis regarding certain topological properties
of operator 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 due to von Neumann (1930).
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.
-Algebras and von Neumann Algebras." Feb. 8, 2017.