On bi-quasitriangular operators
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- by L. J. Gray PDF
- Proc. Amer. Math. Soc. 64 (1977), 291-294 Request permission
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.References
- Constantin Apostol and Norberto Salinas, Nilpotent approximations and quasinilpotent operators, Pacific J. Math. 61 (1975), no. 2, 327–337. MR 415373
- Constantin Apostol and Joseph Stampfli, On derivation ranges, Indiana Univ. Math. J. 25 (1976), no. 9, 857–869. MR 412890, DOI 10.1512/iumj.1976.25.25067
- L. J. Gray, Jordan representation for a class of nilpotent operators, Indiana Univ. Math. J. 26 (1977), no. 1, 57–64. MR 425653, DOI 10.1512/iumj.1977.26.26003 A. E. Taylor, Functional analysis, Wiley, New York, 1967.
- Dan Voiculescu, Norm-limits of algebraic operators, Rev. Roumaine Math. Pures Appl. 19 (1974), 371–378. MR 343082
- L. R. Williams, Similarity invariants for a class of nilpotent operators, Acta Sci. Math. (Szeged) 38 (1976), no. 3-4, 423–428. MR 430827
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 64 (1977), 291-294
- MSC: Primary 47A65
- DOI: https://doi.org/10.1090/S0002-9939-1977-0454698-X
- MathSciNet review: 0454698