Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
MathSciNet review: 0417834
Full-text PDF Free Access

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.

References [Enhancements On Off] (What's this?)

  • [1] S. R. Caradus, W. E. Pfaffenberger and B. Yood, Calkin algebras and algebras of operators on Banach spaces, Lecture Notes in Pure and Appl. Math., no. 9, Dekker, New York, 1974. MR 0415345 (54:3434)
  • [2] T. A. Gillespie and T. T. West, A characterisation and two examples of Riesz operators, Glasgow Math. J. 9 (1968), 106-110. MR 38 #5031. MR 0236737 (38:5031)
  • [3] I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonseljadjoint operators, ``Nauka", Moscow, 1965; English transl., Transl. Math. Monographs, vol. 18, Amer. Math. Soc., Providence, R. I., 1969. MR 36 #3137; 39 #7447. MR 0246142 (39:7447)
  • [4] J. G. Stampfli, Compact perturbations, normal eigenvalues and a problem of Salinas, J. London Math. Soc. (2) 9 (1974/75), 165-175. MR 51 #1449. MR 0365196 (51:1449)
  • [5] T. T. West, The decomposition of Riesz operators, Proc. London Math. Soc. (3) 16 (1966), 737-752. MR 33 #6417. MR 0198258 (33:6417)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B05

Retrieve articles in all journals with MSC: 47B05

Additional Information

Keywords: Riesz operators, quasinilpotent operators
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society