대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제56권2호
  • /
  • Pages.319-331
  • /
  • 2019
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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COMPACT SUMS OF TOEPLITZ PRODUCTS ON WEIGHTED DIRICHLET SPACE OF THE UNIT BALL

  • Hu, Yinyin (Department of Mathematics Dalian Maritime university) ;
  • Lu, Yufeng (School of Mathematical Sciences Dalian University of Technology)
  • 투고 : 2018.01.07
  • 심사 : 2019.03.04
  • 발행 : 2019.03.31
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⟨ 이전 논문 다음 논문 ⟩

초록

On the weighted Dirichlet space, by the Sobolev's embedding theorem, we characterize the compactness for operators which are finite sums of products of several Toeplitz operators. Moreover, the essential spectrum of Toeplitz operator is characterized.

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과제정보

연구 과제 주관 기관 : NSFC

참고문헌

  1. T. Le, Compact Toeplitz operators with continuous symbols, Glasg. Math. J. 51 (2009), no. 2, 257-261. https://doi.org/10.1017/S0017089508004679
  2. T. Le, 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
  3. Y. J. Lee, Algebraic properties of Toeplitz operators on the Dirichlet space, J. Math. Anal. Appl. 329 (2007), no. 2, 1316-1329. https://doi.org/10.1016/j.jmaa.2006.07.041
  4. Y. J. Lee and K. Na, Compact sums of Toeplitz products on weighted Bergman and Dirichlet spaces, Complex Anal. Oper. Theory 10 (2016), no. 8, 1799-1809. https://doi.org/10.1007/s11785-016-0576-x
  5. T. Nakazi and M. Yamada, Riesz's functions in weighted Hardy and Bergman spaces, Canad. J. Math. 48 (1996), no. 5, 930-945. https://doi.org/10.4153/CJM-1996-048-5
  6. T. Nakazi and R. Yoneda, Compact Toeplitz operators with continuous symbols on weighted Bergman spaces, Glasg. Math. J. 42 (2000), no. 1, 31-35. https://doi.org/10.1017/S0017089500010053
  7. T. Yu, Toeplitz operators on the Dirichlet space, Integral Equations Operator Theory 67 (2010), no. 2, 163-170. https://doi.org/10.1007/s00020-010-1754-2