The commutant of L(H) in its ultrapower may or may not be trivial
  Kirchberg asked in 2004 whether the commutant of L(H)$ in its (norm) ultrapower is trivial. Assuming the Continnuum Hypothesis, we prove that the answer depends on the choice of the ultrafilter. 
Ilijas Farah, N. Christopher Phillips, Juris Stepr\=ans