Bicommutant
In algebra, the bicommutant of a subset  of a group is the commutant of the commutant of that subset. It is also known as the double commutant or second commutant and is written  .
The bicommutant of always contains . Since  , it follows that the commutant of the bicommutant of is equal to the commutant of . Thus we have
 ,
 .
See also von Neumann double commutant theorem.
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