DOI QR코드

DOI QR Code

ON RANK ONE PERTURBATIONS OF THE UNILATERAL SHIFT

  • Ko, Eung-Il (DEPARTMENT OF MATHEMATICS EWHA WOMEN'S UNIVERSITY) ;
  • Lee, Ji-Eun (DEPARTMENT OF MATHEMATICS KYUNG HEE UNIVERSITY, INSTITUTE OF MATHEMATICAL SCIENCES EWHA WOMEN'S UNIVERSITY)
  • Received : 2009.12.19
  • Published : 2011.01.31

Abstract

In this paper we study some properties of rank one perturbations of the unilateral shift operators $T=S+u{\otimes}{\upsilon}$. In particular, we give some criteria for eigenvalues of T. Also we characterize some conditions for T to be hyponormal.

Acknowledgement

Supported by : Korea Research Foundation

References

  1. A. Brown, On a class of operators, Proc. Amer. Math. Soc. 4 (1953), 723-728. https://doi.org/10.1090/S0002-9939-1953-0059483-2
  2. A. Brown and C. Pearcy, Spectra of tensor products of operators, Proc. Amer. Math. Soc. 17 (1966), 162-166. https://doi.org/10.1090/S0002-9939-1966-0188786-5
  3. G. Cassier and D. Timotin, Power boundedness and similarity to contractions for some perturbations of isometries, J. Math. Anal. Appl. 293 (2004), no. 1, 160-180. https://doi.org/10.1016/j.jmaa.2003.12.020
  4. J. B. Conway, Subnormal operators, Pitman, London, 1981.
  5. J. B. Conway, A Course in Functional Analysis, Springer-Verlag, 1985.
  6. N. Dunford and J. Schwarz, Linear Operators III, John Wiley and Sons, 1971.
  7. P. R. Halmos, A Hilbert Space Problem Book, Springer-Verlag Berlin Heidelberg New York, 1980.
  8. E. Ionascu, Rank-one perturbations of diagonal operators, Integral Equations Operator Theory 39 (2001), no. 4, 421-440. https://doi.org/10.1007/BF01203323
  9. I. Jung, E. Ko, and C. Pearcy, Aluthge transforms of operators, Integral Equations Operator Theory 37 (2000), no. 4, 437-448. https://doi.org/10.1007/BF01192831
  10. C. Kitai, Invariant closed sets for linear operators, Ph. D. Thesis, Univ. of Toronto, 1982.
  11. M. Martin and M. Putinar, Lectures on Hyponormal Operators, Operator Theory: Advances and Applications, 39. Birkhauser Verlag, Basel, 1989.
  12. Y. Nakamura, One-dimensional perturbations of the shift, Integral Equations Operator Theory 17 (1993), no. 3, 373-403. https://doi.org/10.1007/BF01200292
  13. H. Radjavi and P. Rosenthal, Invariant Subspaces, Springer-Verlag, 1973.
  14. J. Stampfli, Perturbations of the shift, J. London Math. Soc. 40 (1965), 345-347. https://doi.org/10.1112/jlms/s1-40.1.345
  15. J. Stampfli, One-dimensional perturbations of operators, Pacific J. Math. 115 (1984), no. 2, 481-491. https://doi.org/10.2140/pjm.1984.115.481