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On quasinilpotent semigroups of operators

Author: P. S. Guinand
Journal: Proc. Amer. Math. Soc. 86 (1982), 485-486
MSC: Primary 47D05
MathSciNet review: 671220
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Abstract: We construct a pair of operators such that the semigroup generated by them consists of operators which are nilpotent of index 3. The sum of the two operators, however, is not quasinilpotent.

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

  • [1] Paul R. Halmos, A Hilbert space problem book, Van Nostrand, Princeton, N. J., 1967. MR 0208368 (34:8178)
  • [2] Irving Kaplansky, The Engel-Kolchin theorem revisited, Contributions to Algebra, Academic Press, New York, 1977, pp. 233-237. MR 0463200 (57:3156)
  • [3] C. Laurie, E. Nordgren, H. Radjavi and P. Rosenthal, On triangularization of algebras of operators, J. Reine Angew. Math. 327 (1981), 143-155. MR 631313 (83d:47014)
  • [4] J. Levitzki, Über nilpotente Unteringe, Math. Ann. 105 (1931), 620-627. MR 1512728
  • [5] A. Thue, Ueber unendliche Zeichenreihen, Selected Mathematical Papers of Axel Thue, Universiteforlaget, Oslo-Bergen-Tromso, 1977, pp. 139-158.

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