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

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대한수학회 (The Korean Mathematical Society)|2023.01|대한수학회보 (Bulletin of the KMS)|제60권 제1호|pp. 161-170|DOI 10.4134/BKMS.b220042

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참고문헌

키워드

Dirichlet spaceDual Toeplitz operatordual Hankel operator
주제분류수학

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.

Abstract

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.

참고문헌 (12)

  1. Lakhdar Benaissa, "PROPERTIES OF DUAL TOEPLITZ OPERATORS WITH APPLICATIONS TO HAPLITZ PRODUCTS ON THE HARDY SPACE OF THE POLYDISK", Taiwanese Journal of Mathematics, 19(1) (2015), The Mathematical Society of the Republic of China[DOI]
  2. Yong Chen, "Toeplitz and Hankel operators with L∞,1 symbols on Dirichlet space", Journal of Mathematical Analysis and Applications, 369(1), pp.368~376 (2010), Elsevier BV[DOI]
  3. Caixing Gu, "Products of block Toeplitz operators", Pacific Journal of Mathematics, 185(1), pp.115~148 (1998), Mathematical Sciences Publishers[DOI]
  4. Hocine Guediri, "Dual Toeplitz operators on the sphere", Acta Mathematica Sinica, English Series, 29(9), pp.1791~1808 (2013), Springer Science and Business Media LLC[DOI]
  5. L. Kong, "Some algebraic properties of dual Toeplitz operators", Houston J. Math, 44(1), pp.169~185 (2018)
  6. Young Joo Lee, "Algebraic properties of Toeplitz operators on the Dirichlet space", Journal of Mathematical Analysis and Applications, 329(2), pp.1316~1329 (2007), Elsevier BV[DOI]
  7. Young Joo Lee, "Sums of Products of Toeplitz and Hankel Operators on the Dirichlet Space", Integral Equations and Operator Theory, 71(2), pp.275~302 (2011), Springer Science and Business Media LLC[DOI]
  8. Karel Stroethoff, "Algebraic and spectral properties of dual Toeplitz operators", Transactions of the American Mathematical Society, 354(6), pp.2495~2520 (2002), American Mathematical Society (AMS)[DOI]
  9. Z. Wu, "Function theory and operator theory on the Dirichlet space, in Holomorphic spaces (Berkeley, CA, 1995)", Math. Sci. Res. Inst. Publ, 33, pp.179~199 (1998), Cambridge Univ. Press
  10. Tao Yu, "Operators on the orthogonal complement of the Dirichlet space", Journal of Mathematical Analysis and Applications, 357(1), pp.300~306 (2009), Elsevier BV[DOI]
  11. Tao Yu, "Operators on the orthogonal complement of the Dirichlet space (II)", Science China Mathematics, 54(9), pp.2005~2012 (2011), Springer Science and Business Media LLC[DOI]
  12. Tao Yu, "Commuting dual Toeplitz operators on the orthogonal complement of the Dirichlet space", Acta Mathematica Sinica, English Series, 25(2), pp.245~252 (2009), Springer Science and Business Media LLC[DOI]

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