The commutant 
of a subset 
, where 
is a complex Hilbert
space and 
is the space of continuous linear operators on it, is the collection of all
elements of 
that commute with every element of 
:
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Across the literature on the subject, the set 
is sometimes denoted 
, a reference to the fact that a linear
operator between normed spaces is continuous iff it is bounded (Royden
and Fitzpatrick 2010).
The notions of commutant and bicommutant are fundamental to the study of von Neumann algebras (Dixmier 1981).
