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Proceedings of the American Mathematical Society

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On bi-quasitriangular operators

Author: L. J. Gray
Journal: Proc. Amer. Math. Soc. 64 (1977), 291-294
MSC: Primary 47A65
MathSciNet review: 0454698
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Abstract: It is shown that the set of nilpotent operators T for which $ {T^k}$ has closed range for all k is norm dense in the set of all nilpotent operators. A consequence of this is that every bi-quasitriangular operator is a norm limit of operators which are similar to a direct sum of weighted shifts plus scalars.

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  • [1] C. Apostol and N. Salinas, Nilpotent approximations and quasinilpotent operators, Pacific J. Math. 61 (1975), 327-337. MR 0415373 (54:3461)
  • [2] C. Apostol and J. G. Stampfli, On derivation ranges, Indiana J. Math. 25 (1976), 857-870. MR 0412890 (54:1011)
  • [3] L. J. Gray, Jordan representation for a class of nilpotent operators, Indiana J. Math. 26 (1977), 57-64. MR 0425653 (54:13607)
  • [4] A. E. Taylor, Functional analysis, Wiley, New York, 1967.
  • [5] D. Voiculescu, Norm-limits of algebraic operators, Rev. Roumaine Math. Pures Appl. 19 (1974), 371-378. MR 49 #7826. MR 0343082 (49:7826)
  • [6] L. Williams, Similarity invariants for a class of nilpotent operators (to appear). MR 0430827 (55:3832)

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Keywords: Bi-quasitriangular, nilpotent operator, algebraic operator, closed range
Article copyright: © Copyright 1977 American Mathematical Society

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