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Journal of Function Spaces
Volume 2017 (2017), Article ID 5807909, 4 pages
https://doi.org/10.1155/2017/5807909
Research Article

A Note on Reducing Subspaces of Toeplitz Operator on the Weighted Analytic Function Spaces of the Bidisk

College of Computer and Information Sciences, Fujian Agriculture and Forestry University, Fujian 350002, China

Correspondence should be addressed to Hongzhao Lin

Received 22 February 2017; Accepted 28 March 2017; Published 7 May 2017

Academic Editor: Raúl E. Curto

Copyright © 2017 Hongzhao Lin. 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. Stessin and K. Zhu, “Reducing subspaces of weighted shift operators,” Proceedings of the American Mathematical Society, vol. 130, no. 9, pp. 2631–2639, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. K. Zhu, “Reducing subspaces for a class of multiplication operators,” Journal of the London Mathematical Society. Second Series, vol. 62, no. 2, pp. 553–568, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  3. K. Guo, S. Sun, D. Zheng, and C. Zhong, “Multiplication operators on the Bergman space via the Hardy space of the bidisk,” Journal für die Reine und Angewandte Mathematik. [Crelle's Journal], vol. 628, pp. 129–168, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  4. K. Guo and H. Huang, “On multiplication operators on the Bergman space: similarity, unitary equivalence and reducing subspaces,” Journal of Operator Theory, vol. 65, no. 2, pp. 355–378, 2011. View at Google Scholar · View at MathSciNet · View at Scopus
  5. Y. Lu and X. Zhou, “Invariant subspaces and reducing subspaces of weighted Bergman space over bidisk,” Journal of the Mathematical Society of Japan, vol. 62, no. 3, pp. 745–765, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. X. Zhou, Y. Shi, and Y. Lu, “Invariant subspaces and reducing subspaces of weighted Bergman space over polydisc,” Science China Mathematics, vol. 41, no. 5, pp. 427–438, 2011. View at Publisher · View at Google Scholar
  7. Y. Shi and Y. Lu, “Reducing subspaces for Toeplitz operators on the polydisk,” Bulletin of the Korean Mathematical Society, vol. 50, no. 2, pp. 687–696, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. H. Z. Lin, Y. Y. Hu, and Y. F. Lu, “Reducing subspaces of Toeplitz operator on the weighted dirichlet space of the bidisk,” Chinese Annals of Mathematics. Series A, vol. 37, no. 3, pp. 311–328, 2016. View at Google Scholar · View at MathSciNet