DOI QR코드

DOI QR Code

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)
  • Received : 2018.01.07
  • Accepted : 2019.03.04
  • Published : 2019.03.31

Abstract

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.

Acknowledgement

Supported by : NSFC

References

  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