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Double commutants of algebraic operators

Author: T. Rolf Turner
Journal: Proc. Amer. Math. Soc. 33 (1972), 415-419
MSC: Primary 47A65; Secondary 46L99
Erratum: Proc. Amer. Math. Soc. 45 (1974), 466.
MathSciNet review: 0291863
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Abstract: The double commutant of an algebraic operator on a complex Hilbert space is equal to the algebra (with identity) generated by that operator.

References [Enhancements On Off] (What's this?)

  • [1] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Gauthier-Villars, Paris, 1969.
  • [2] Nathan Jacobson, Lectures in abstract algebra. Vol. II. Linear algebra, D. Van Nostrand Co., Inc., Toronto-New York-London, 1953. MR 0053905
  • [3] Irving Kaplansky, Infinite abelian groups, Revised edition, The University of Michigan Press, Ann Arbor, Mich., 1969. MR 0233887
  • [4] Marvin Rosenblum, On the operator equation 𝐵𝑋-𝑋𝐴=𝑄, Duke Math. J. 23 (1956), 263–269. MR 0079235
  • [5] N. Salinas and D. Herrero, Analytically invariant and bi-variant subspaces (to appear).

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Keywords: Double commutant, algebraic, nilpotent, invariant subspace
Article copyright: © Copyright 1972 American Mathematical Society

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