Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 902853, 8 pages
http://dx.doi.org/10.1155/2012/902853
Research Article

A Note on Unbounded Hyponormal Composition Operators in -Spaces

Katedra Zastosowań Matematyki, Uniwersytet Rolniczy w Krakowie, ul. Balicka 253c, 30-189 Kraków, Poland

Received 27 September 2012; Revised 23 October 2012; Accepted 5 November 2012

Academic Editor: Anna Kamińska

Copyright © 2012 Piotr Budzyński. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Z. J. Jabłoński, I. B. Jung, and J. Stochel, “A non-hyponormal operator generating Stieltjes moment sequences,” Journal of Functional Analysis, vol. 262, no. 9, pp. 3946–3980, 2012. View at Publisher · View at Google Scholar
  2. J. T. Campbell and W. E. Hornor, “Seminormal composition operators,” Journal of Operator Theory, vol. 29, no. 2, pp. 323–343, 1993. View at Google Scholar · View at Zentralblatt MATH
  3. Z. J. Jabłoński, “Hyperexpansive composition operators,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 135, no. 3, pp. 513–526, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. P. Budzyński, Z. J. Jabłoński, I. B. Jung, and J. Stochel, “On unbounded composition operators in L2-spaces,” Annali di Matematica Pura ed Applicata. In press. View at Publisher · View at Google Scholar
  5. P. Budzyński, Z. J. Jabłoński, I. B. Jung, and J. Stochel, “Unbounded subnormal composition operators in L2-spaces,” in preparation.
  6. A. Lambert, “Subnormal composition operators,” Proceedings of the American Mathematical Society, vol. 103, no. 3, pp. 750–754, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. E. Bishop, “Spectral theory for operators on a Banach space,” Transactions of the American Mathematical Society, vol. 86, pp. 414–445, 1957. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. C. Foiaş, “Décompositions en opérateurs et vecteurs propres. I. Études de ces décompositions et leurs rapports avec les prolongements des opérateurs,” Revue Roumaine de Mathématique Pures et Appliquées, vol. 7, pp. 241–282, 1962. View at Google Scholar · View at Zentralblatt MATH
  9. F. H. Szafraniec, “Sesquilinear selection of elementary spectral measures and subnormality,” in Elementary Operators and Applications (Blaubeuren, 1991), pp. 243–248, World Scientific, River Edge, NJ, USA, 1992. View at Google Scholar
  10. F. H. Szafraniec, “On normal extensions of unbounded operators. IV. A matrix construction,” in Operator Theory and Indefinite Inner Product Spaces, vol. 163 of Operator Theory: Advances and Applications, pp. 337–350, Birkhäuser, Basel, Switzerland, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. Z. J. Jablonski, I. B. Jung, and J. Stochel, “A hyponormal weighted shift on a directed tree whose square has trivial domain,” http://arxiv.org/abs/1104.5195.
  12. J. Janas, “On unbounded hyponormal operators,” Arkiv för Matematik, vol. 27, no. 2, pp. 273–281, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. J. Janas, “On unbounded hyponormal operators. II,” Integral Equations and Operator Theory, vol. 15, no. 3, pp. 470–478, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. J. Janas, “On unbounded hyponormal operators. III,” Studia Mathematica, vol. 112, no. 1, pp. 75–82, 1994. View at Google Scholar · View at Zentralblatt MATH
  15. E. A. Nordgren, “Composition operators on Hilbert spaces,” in Hilbert Space Operators, vol. 693 of Lecture Notes in Mathematics, pp. 37–63, Springer, Berlin, Germany, 1978. View at Google Scholar · View at Zentralblatt MATH
  16. R. K. Singh and J. S. Manhas, Composition Operators on Function Spaces, vol. 179 of North-Holland Mathematics Studies, Elsevier Science Publishers B.V., North-Holland, Amsterdam, The Netherlands, 1993.
  17. R. K. Singh and A. Kumar, “Characterizations of invertible, unitary, and normal composition operators,” Bulletin of the Australian Mathematical Society, vol. 19, no. 1, pp. 81–95, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. R. Whitley, “Normal and quasinormal composition operators,” Proceedings of the American Mathematical Society, vol. 70, no. 2, pp. 114–118, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. D. J. Harrington and R. Whitley, “Seminormal composition operators,” Journal of Operator Theory, vol. 11, no. 1, pp. 125–135, 1984. View at Google Scholar · View at Zentralblatt MATH
  20. A. Lambert, “Hyponormal composition operators,” The Bulletin of the London Mathematical Society, vol. 18, no. 4, pp. 395–400, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. C. Burnap, I. B. Jung, and A. Lambert, “Separating partial normality classes with composition operators,” Journal of Operator Theory, vol. 53, no. 2, pp. 381–397, 2005. View at Google Scholar · View at Zentralblatt MATH
  22. P. Budzyński and J. Stochel, “Joint subnormality of n-tuples and C0-semigroups of composition operators on L2-spaces. II,” Studia Mathematica, vol. 193, no. 1, pp. 29–52, 2009. View at Publisher · View at Google Scholar
  23. M. M. Rao, Conditional Measures and Applications, vol. 271 of Pure and Applied Mathematics (Boca Raton), Chapman & Hall/CRC, Boca Raton, Fla, USA, 2005. View at Publisher · View at Google Scholar
  24. M. Naimark, “On the square of a closed symmetric operator,” Doklady Akademii Nauk SSSR, vol. 26, pp. 866–870, 1940. View at Google Scholar · View at Zentralblatt MATH
  25. M. Naimark, “On the square of a closed symmetric operator,” Doklady Akademii Nauk SSSR, vol. 28, pp. 207–208, 1940. View at Google Scholar
  26. I. B. Jung, P. S. Lim, and S. S. Park, “Gaps of operators,” Journal of Mathematical Analysis and Applications, vol. 304, no. 1, pp. 87–95, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. I. B. Jung, M. R. Lee, and P. S. Lim, “Gaps of operators. II,” Glasgow Mathematical Journal, vol. 47, no. 3, pp. 461–469, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. C. Burnap and I. B. Jung, “Composition operators with weak hyponormality,” Journal of Mathematical Analysis and Applications, vol. 337, no. 1, pp. 686–694, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  29. G. Exner, I. B. Jung, and M. R. Lee, “Block matrix operators and weak hyponormalities,” Integral Equations and Operator Theory, vol. 65, no. 3, pp. 345–362, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH