Double commutants of algebraic operators
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- by T. Rolf Turner
- Proc. Amer. Math. Soc. 33 (1972), 415-419
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291863-4
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Erratum: Proc. Amer. Math. Soc. 45 (1974), 466.
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
- J. Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien, Gauthier-Villars, Paris, 1969.
- Nathan Jacobson, Lectures in abstract algebra. Vol. II. Linear algebra, D. Van Nostrand Co., Inc., Toronto-New York-London, 1953. MR 0053905
- Irving Kaplansky, Infinite abelian groups, Revised edition, University of Michigan Press, Ann Arbor, Mich., 1969. MR 0233887
- Marvin Rosenblum, On the operator equation $BX-XA=Q$, Duke Math. J. 23 (1956), 263–269. MR 79235 N. Salinas and D. Herrero, Analytically invariant and bi-variant subspaces (to appear).
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 415-419
- MSC: Primary 47A65; Secondary 46L99
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291863-4
- MathSciNet review: 0291863