 
Summary: Free Entropy Dimension in finite von
Neumann Algebras
Junhao Shen
von Neumann algebras
Let H be a separable complex Hilbert space.
Let B(H) be the set of all bounded linear
operators from H to H.
The adjoint of a bounded linear operator
T is the operator T characterized by the
identity
< Tv, w >=< v, Tw > v, w H.
Weak operator topology (WOT) on B(H)
is the topology such that a sequence (or
a net) {T} converges to T in the weak
operator topology if and only if
Tv1, v2 Tv1, v2
for all v1, v2 H.
A von Neumann algebra M is defined to
be a selfadjoint subalgebra of B(H) which
is closed in weak operator topology, i.e.
