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J. Math. Phys. 28, 1 (1987); http://dx.doi.org/10.1063/1.527789 (7 pages)
Commutants and bicommutants of algebras of unbounded operators
(Received 24 April 1986; accepted 17 September 1986)
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Add to FacebookThe first purpose of this paper is to show that for each Op∗‐algebra (M,D) whose weak commutant M′w is an algebra, there exists a closed Op∗‐algebra (M,D), which is the smallest extension of (M,D) satisfying Mw =M′w and Mw D =D. The second purpose is to characterize an unbounded bicommutant M″wσ of an Op∗‐algebra M. The third purpose is to generalize the well‐known Radon–Nikodym theorem for von Neumann algebras to Op∗‐algebras M satisfying the von Neumann density type theorem M t∗s =M″wσ.
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