대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제50권2호
  • /
  • Pages.687-696
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  • 2013
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2012.01.25
  • 발행 : 2013.03.31
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⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

참고문헌

  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.
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  3. Y. Lu and Y. Shi, Hyponormal Toeplitz operators on the weighted Bergman space, Integral Equations Operator Theory 65 (2009), no. 1, 115-129. https://doi.org/10.1007/s00020-009-1712-z
  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. https://doi.org/10.2969/jmsj/06230745
  5. S. Shimorin, On Beurling-type theorems in weighted $l^{2}$ and Bergman spaces, Proc. Amer. Math. Soc. 131 (2003), no. 6, 1777-1787. https://doi.org/10.1090/S0002-9939-02-06721-7
  6. L. Trieu, On Toeplitz operators on Bergman spaces of the unit polydisk, Proc. Amer. Math. Soc. 138 (2010), no. 1, 275-285. https://doi.org/10.1090/S0002-9939-09-10060-6
  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. https://doi.org/10.1360/012010-627
  8. K. Zhu, Reducing subspaces for a class of multiplication operators, J. London Math. Soc. 62 (2000), no. 2, 553-568. https://doi.org/10.1112/S0024610700001198
  9. K. Zhu, Operator Theory in Function Spaces, 2nd ed. Providence, R.I.: American Mathematical Society, 2007.

피인용 문헌

  1. Reducing subspaces of tensor products of weighted shifts vol.59, pp.4, 2016, https://doi.org/10.1007/s11425-015-5089-y
  2. A Note on Reducing Subspaces of Toeplitz Operator on the Weighted Analytic Function Spaces of the Bidisk Hw2D2 vol.2017, 2017, https://doi.org/10.1155/2017/5807909
  3. REDUCING SUBSPACES FOR A CLASS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THE BIDISK vol.52, pp.5, 2015, https://doi.org/10.4134/BKMS.2015.52.5.1649
  4. Multiplication Operators Defined by a Class of Polynomials on $${L_a^2(\mathbb{D}^2)}$$ L a 2 ( D 2 ) vol.80, pp.4, 2014, https://doi.org/10.1007/s00020-014-2176-3
  5. Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk vol.2015, 2015, https://doi.org/10.1155/2015/209307
  6. Reducing subspaces for a class of non-analytic Toeplitz operators on the bidisk vol.445, pp.1, 2017, https://doi.org/10.1016/j.jmaa.2016.08.012
  7. Reducing subspaces of multiplication operators with the symbol αz k + βw l on $$L_a^2 (\mathbb{D}^2 )$$ vol.58, pp.10, 2015, https://doi.org/10.1007/s11425-015-4973-9
  8. Joint Reducing Subspaces of Multiplication Operators and Weight of Multi-variable Bergman Spaces vol.40, pp.2, 2019, https://doi.org/10.1007/s11401-019-0125-9