A note on Riesz operators

Chui, C. K.; Smith, P. W.; Ward, J. D.

doi:10.1090/S0002-9939-1976-0417834-6

A note on Riesz operators
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by C. K. Chui, P. W. Smith and J. D. Ward PDF

Proc. Amer. Math. Soc. 60 (1976), 92-94 Request permission

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