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Reducing subspaces for Toeplitz operators on the polydisk

Yufeng Lu|Yanyue Shi
대한수학회 (The Korean Mathematical Society)|2013.03|대한수학회보 (Bulletin of the KMS)|제50권 제2호|pp. 687-696

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참고문헌

키워드

Toeplitz operatorBergman spacereducing subspace
주제분류수학

초록

In this note, we completely characterize the reducing sub- spaces of TzN 1 zM 2 on A2 α(D2) where α> −1 and N,M are positive in- tegers with N ≠ M, and show that the minimal reducing subspaces of TzN 1 zM 2 on the unweighted Bergman space and on the weighted Bergman space are different.

Abstract

In this note, we completely characterize the reducing sub- spaces of TzN 1 zM 2 on A2 α(D2) where α> −1 and N,M are positive in- tegers with N ≠ M, and show that the minimal reducing subspaces of TzN 1 zM 2 on the unweighted Bergman space and on the weighted Bergman space are different.

참고문헌 (9)

  1. K. Guo, "On Multiplication operators on the Bergman space: similarity, unitary equivalence and reducing subspaces", J. Operator Theory, 65(2), pp.355~378 (2011)
  2. K. Guo, "Multiplication operators on the Bergman space via the Hardy space of the bidisk", J. Reine Angew. Math, 628, pp.129~168 (2009)
  3. Y. Lu, "Hyponormal Toeplitz operators on the weighted Bergman space", Integral Equations Operator Theory, 65(1), pp.115~129 (2009)
  4. Y. Lu, "Invariant subspaces and reducing subspaces of weighted Bergman space over bidisk", J. Math. Soc. Japan, 62(3), pp.745~765 (2010)
  5. S. Shimorin, "On Beurling-type theorems in weighted l2 and Bergman spaces", Proc. Amer. Math. Soc, 131(6), pp.1777~1787 (2003)
  6. L. Trieu, "On Toeplitz operators on Bergman spaces of the unit polydisk", Proc. Amer. Math. Soc, 138(1), pp.275~285 (2010)
  7. X. Zhou, "Invariant subspaces and reducing subspaces of weighted Bergman space over polydisc", Sci. Sin. Math, 41(5), pp.427~438 (2011)
  8. K. Zhu, "Reducing subspaces for a class of multiplication operators", J. London Math. Soc, 62(2), pp.553~568 (2000)
  9. K. Zhu, "Operator Theory in Function Spaces, 2nd ed" (2007), American Math-ematical Society

관련 논문AI추천

REDUCING SUBSPACES FOR A CLASS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THE BIDISKMohammed Albaseer, Yanyue Shi, Yufeng Lu대한수학회 · 대한수학회보2015 · 제52권 제5호Reducing subspaces for a class of Toeplitz operators on weighted Hardy spaces over bidiskShuhei Kuwahara대한수학회 · 대한수학회보2017 · 제54권 제4호Reducing subspaces of a class of multiplication operatorsBin Liu, Yanyue Shi대한수학회 · 대한수학회보2017 · 제54권 제4호Fredholm Toeplitz operators on the Dirichlet spaces of the polydisk나경욱대한수학회 · 대한수학회보2020 · 제57권 제2호The Hyponormal Toeplitz operators on the vector valued Bergman spacePuyu Cui, Yanyue Shi, Yufeng Lu대한수학회 · 대한수학회보2014 · 제51권 제1호Some Toeplitz operators on weighted Bergman spaces강시호대한수학회 · 대한수학회보2011 · 제48권 제1호

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