DOI QR코드

DOI QR Code

ZERO SUMS OF DUAL TOEPLITZ PRODUCTS ON THE ORTHOGONAL COMPLEMENT OF THE DIRICHLET SPACE

  • Young Joo, Lee (Department of Mathematics Chonnam National University)
  • 투고 : 2022.01.13
  • 심사 : 2022.06.08
  • 발행 : 2023.01.31

초록

We consider dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space on the unit disk. We give a characterization of when a finite sum of products of two dual Toeplitz operators is equal to 0. Our result extends several known results by using a unified way.

키워드

과제정보

The author would like to thank the referee for the helpful comments and suggestions.

참고문헌

  1. L. Benaissa and H. Guediri, Properties of dual Toeplitz operators with applications to Haplitz products on the Hardy space of the polydisk, Taiwanese J. Math. 19 (2015), no. 1, 31-49. https://doi.org/10.11650/tjm.19.2015.4323
  2. Y. Chen and N. Q. Dieu, Toeplitz and Hankel operators with L∞,1 symbols on Dirichlet space, J. Math. Anal. Appl. 369 (2010), no. 1, 368-376. https://doi.org/10.1016/j.jmaa.2010.03.025
  3. C. Gu and D. Zheng, Products of block Toeplitz operators, Pacific J. Math. 185 (1998), no. 1, 115-148. https://doi.org/10.2140/pjm.1998.185.115
  4. H. Guediri, Dual Toeplitz operators on the sphere, Acta Math. Sin. (Engl. Ser.) 29 (2013), no. 9, 1791-1808. https://doi.org/10.1007/s10114-013-1717-z
  5. L. Kong and Y. Lu, Some algebraic properties of dual Toeplitz operators, Houston J. Math. 44 (2018), no. 1, 169-185.
  6. 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
  7. Y. J. Lee and K. Zhu, Sums of products of Toeplitz and Hankel operators on the Dirichlet space, Integral Equations Operator Theory 71 (2011), no. 2, 275-302. https://doi.org/10.1007/s00020-011-1901-4
  8. K. Stroethoff and D. Zheng, Algebraic and spectral properties of dual Toeplitz operators, Trans. Amer. Math. Soc. 354 (2002), no. 6, 2495-2520. https://doi.org/10.1090/S0002-9947-02-02954-9
  9. Z. Wu, Function theory and operator theory on the Dirichlet space, in Holomorphic spaces (Berkeley, CA, 1995), 179-199, Math. Sci. Res. Inst. Publ., 33, Cambridge Univ. Press, Cambridge, 1998.
  10. T. Yu, Operators on the orthogonal complement of the Dirichlet space, J. Math. Anal. Appl. 357 (2009), no. 1, 300-306. https://doi.org/10.1016/j.jmaa.2009.04.019
  11. T. Yu, Operators on the orthogonal complement of the Dirichlet space (II), Sci. China Math. 54 (2011), no. 9, 2005-2012. https://doi.org/10.1007/s11425-011-4259-9
  12. T. Yu and S. Y. Wu, Commuting dual Toeplitz operators on the orthogonal complement of the Dirichlet space, Acta Math. Sin. (Engl. Ser.) 25 (2009), no. 2, 245-252. https://doi.org/10.1007/s10114-008-7109-0