The bicentralizer 
of a von Neumann algebra with a faithful normal
state is the set of 
that asymptotically commute with every uniformly bounded
sequence 
asymptotically centralizing the state in predual norm.
More explicitly, its defining implication is
 |
The module conventions are 
and 
. For a tracial
state, every bounded sequence centralizes
the state, so the bicentralizer is the center of 
. The bicentralizer conjecture
asks for 
for type 
factors with separable predual.
