A note on Riesz operators
Authors:
C. K. Chui, P. W. Smith and J. D. Ward
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
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Abstract | References | Similar Articles | Additional Information
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.
- S. R. Caradus, W. E. Pfaffenberger, and Bertram Yood, Calkin algebras and algebras of operators on Banach spaces, Marcel Dekker, Inc., New York, 1974. Lecture Notes in Pure and Applied Mathematics, Vol. 9. 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 https://doi.org/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 https://doi.org/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 https://doi.org/10.1112/plms/s3-16.1.737
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Keywords:
Riesz operators,
quasinilpotent operators
Article copyright:
© Copyright 1976
American Mathematical Society
