Commutant
Given a complex Hilbert space H with associated space L(H) of continuous linear operators from H to itself, the commutant M^' of an arbitrary subset M subset= L(H) is the collection of all elements in L(H) which commute with all elements of M: M^'={T in L(H):TS=ST for all S in M}.
Across the literature on the subject, the set L(H) is sometimes denoted B(H), a reference to the fact that a linear operator between normed vector spaces is continuous if and only if it is bounded (Royden and Fitzpatrick 2010).
The notions of commutant and bicommutant are fundamental to the study of von Neumann algebras (Dixmier 1981).
See also
Bicommutant, Bicommutant Theorem, von Neumann Algebra, W-*-AlgebraThis entry contributed by Christopher Stover
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References
Dixmier, J. Von Neumann Algebras. Amsterdam, Netherlands: North-Holland, 1981.Royden, H. L. and Fitzpatrick, P. M. Real Analysis. Pearson, 2010.Referenced on Wolfram|Alpha
CommutantCite this as:
Stover, Christopher. "Commutant." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Commutant.html