A note on Riesz operators
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- by C. K. Chui, P. W. Smith and J. D. Ward
- Proc. Amer. Math. Soc. 60 (1976), 92-94
- DOI: https://doi.org/10.1090/S0002-9939-1976-0417834-6
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Abstract:
The purpose of this note is to settle a problem posed by Caradus, Pfaffenberger, and Yood; namely, it is proved that every Riesz operator R on a Hilbert space has a decomposition $R = C + Q$ where C is compact and both Q and $CQ - QC$ are quasinilpotent.References
- S. R. Caradus, W. E. Pfaffenberger, and Bertram Yood, Calkin algebras and algebras of operators on Banach spaces, Lecture Notes in Pure and Applied Mathematics, Vol. 9, Marcel Dekker, Inc., New York, 1974. MR 0415345
- T. A. Gillespie and T. T. West, A characterization and two examples of Riesz operators, Glasgow Math. J. 9 (1968), 106–110. MR 236737, DOI 10.1017/S0017089500000379
- I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. Translated from the Russian by A. Feinstein. MR 0246142
- Joseph G. Stampfli, Compact perturbations, normal eigenvalues and a problem of Salinas, J. London Math. Soc. (2) 9 (1974/75), 165–175. MR 365196, DOI 10.1112/jlms/s2-9.1.165
- T. T. West, The decomposition of Riesz operators, Proc. London Math. Soc. (3) 16 (1966), 737–752. MR 198258, DOI 10.1112/plms/s3-16.1.737
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 60 (1976), 92-94
- MSC: Primary 47B05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0417834-6
- MathSciNet review: 0417834