Browse > Article
http://dx.doi.org/10.4134/BKMS.2013.50.2.687

REDUCING SUBSPACES FOR TOEPLITZ OPERATORS ON THE POLYDISK  

Shi, Yanyue (College of Mathematical Science Ocean University of China)
Lu, Yufeng (School of Mathematical Sciences Dalian University of Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.2, 2013 , pp. 687-696 More about this Journal
Abstract
In this note, we completely characterize the reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on $A^2_{\alpha}(D^2)$ where ${\alpha}$ > -1 and N, M are positive integers with $N{\neq}M$, and show that the minimal reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on the unweighted Bergman space and on the weighted Bergman space are different.
Keywords
Toeplitz operator; reducing subspace; Bergman space;
Citations & Related Records
연도 인용수 순위
  • Reference
1 K. Guo and H. Huang, On Multiplication operators on the Bergman space: similarity, unitary equivalence and reducing subspaces, J. Operator Theory 65 (2011), no. 2, 355-378.
2 K. Guo, S. Sun, D. Zheng, and C. Zhong, Multiplication operators on the Bergman space via the Hardy space of the bidisk, J. Reine Angew. Math. 628 (2009), 129-168.
3 Y. Lu and Y. Shi, Hyponormal Toeplitz operators on the weighted Bergman space, Integral Equations Operator Theory 65 (2009), no. 1, 115-129.   DOI
4 Y. Lu and X. Zhou, Invariant subspaces and reducing subspaces of weighted Bergman space over bidisk, J. Math. Soc. Japan 62 (2010), no. 3, 745-765.   DOI
5 S. Shimorin, On Beurling-type theorems in weighted $l^{2}$ and Bergman spaces, Proc. Amer. Math. Soc. 131 (2003), no. 6, 1777-1787.   DOI   ScienceOn
6 L. Trieu, On Toeplitz operators on Bergman spaces of the unit polydisk, Proc. Amer. Math. Soc. 138 (2010), no. 1, 275-285.   DOI   ScienceOn
7 X. Zhou, Y. Shi, and Y. Lu, Invariant subspaces and reducing subspaces of weighted Bergman space over polydisc, Sci. Sin. Math. 41 (2011), no. 5, 427-438.   DOI
8 K. Zhu, Reducing subspaces for a class of multiplication operators, J. London Math. Soc. 62 (2000), no. 2, 553-568.   DOI
9 K. Zhu, Operator Theory in Function Spaces, 2nd ed. Providence, R.I.: American Mathematical Society, 2007.