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Journal of Function Spaces
Volume 2018, Article ID 6078594, 6 pages
https://doi.org/10.1155/2018/6078594
Research Article

On Some Properties of Cowen-Douglas Class of Operators

Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

Correspondence should be addressed to Bahmann Yousefi; ri.ca.unp@ifesuoy_b

Received 9 September 2017; Accepted 29 November 2017; Published 1 February 2018

Academic Editor: Kehe Zhu

Copyright © 2018 Parastoo Heiatian Naeini and Bahmann Yousefi. 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. M. J. Cowen and R. G. Douglas, “Complex geometry and operator theory,” Acta Mathematica, vol. 141, no. 3-4, pp. 187–261, 1978. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. R. E. Curto and N. Salinas, “Generalized Bergman kernels and the Cowen-Douglas theory,” American Journal of Mathematics, vol. 106, no. 2, pp. 447–488, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  3. S. Richter, “Invariant subspaces in Banach spaces of analytic functions,” Transactions of the American Mathematical Society, vol. 304, no. 2, pp. 585–616, 1987. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. K. Seddighi and B. Yousefi, “On the reflexivity of operators on function spaces,” Proceedings of the American Mathematical Society, vol. 116, no. 1, pp. 45–52, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. B. Yousefi and S. Foroutan, “On the multiplication operators on spaces of analytic functions,” Studia Mathematica, vol. 168, no. 2, pp. 187–191, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. K. Zhu, “Operators in Cowen-Douglas classes,” Illinois Journal of Mathematics, vol. 44, no. 4, pp. 767–783, 2000. View at Google Scholar · View at MathSciNet · View at Scopus
  7. K. Zhu, “Irreducible multiplication operators on spaces of analytic functions,” The Journal of Operator Theory, vol. 51, no. 2, pp. 377–385, 2004. View at Google Scholar · View at MathSciNet · View at Scopus
  8. A. L. Shields and L. J. Wallen, “The commutants of certain Hilbert space operators,” Indiana University Mathematics Journal, vol. 20, pp. 777–788, 1970/1971. View at Google Scholar · View at MathSciNet
  9. K. Seddighi, Von Neumann operators in B1(Ω), University of Indiana, 1981.
  10. L. Bagheri and B. Yousefi, “Reflexivity of the shift operator on some BK spaces,” Rendiconti del Circolo Matematico di Palermo Serie II, vol. 63, no. 1, pp. 91–96, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  11. L. Chen, “On intertwining operators via reproducing kernels,” Linear Algebra and its Applications, vol. 438, no. 9, pp. 3661–3666, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. L. Chen, R. G. Douglas, and K. Guo, “On the double commutant of Cowen-Douglas operators,” Journal of Functional Analysis, vol. 260, no. 7, pp. 1925–1943, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. K.-y. Guo and H.-s. Huang, “Reducing subspaces of multiplication operators on function spaces,” Applied Mathematics-A Journal of Chinese Universities Series B, vol. 28, no. 4, pp. 395–404, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. K. Ji, C. Jiang, D. K. Keshari, and G. Misra, “Flag structure for operators in the Cowen-Douglas class,” Comptes Rendus Mathematique, vol. 352, no. 6, pp. 511–514, 2014. View at Google Scholar · View at MathSciNet
  15. A. Koranyi and G. Misra, “A classification of homogeneous operators in the Cowen-Douglas class,” Advances in Mathematics, vol. 226, no. 6, pp. 5338–5380, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  16. B. Yousefi and S. Khoshdel, “Reflexivity of Powers of the Multiplication Operator on Special Function Spaces,” Acta Mathematica Scientia, vol. 32, no. 6, pp. 2279–2284, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. J. B. Conway, The Theory of Subnormal Operators, vol. 36 of Mathematical Surveys and Monographs, American Mathematical Society, Providence‎, ‎RI, USA, 1991. View at Publisher · View at Google Scholar · View at MathSciNet