Kernels of Toeplitz operators on the Bergman space

Young Joo Lee

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 4, page 1119-1130
  • ISSN: 0011-4642

Abstract

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A Coburn theorem says that a nonzero Toeplitz operator on the Hardy space is one-to-one or its adjoint operator is one-to-one. We study the corresponding problem for certain Toeplitz operators on the Bergman space.

How to cite

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Lee, Young Joo. "Kernels of Toeplitz operators on the Bergman space." Czechoslovak Mathematical Journal 73.4 (2023): 1119-1130. <http://eudml.org/doc/299427>.

@article{Lee2023,
abstract = {A Coburn theorem says that a nonzero Toeplitz operator on the Hardy space is one-to-one or its adjoint operator is one-to-one. We study the corresponding problem for certain Toeplitz operators on the Bergman space.},
author = {Lee, Young Joo},
journal = {Czechoslovak Mathematical Journal},
keywords = {Toeplitz operator; Bergman space},
language = {eng},
number = {4},
pages = {1119-1130},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Kernels of Toeplitz operators on the Bergman space},
url = {http://eudml.org/doc/299427},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Lee, Young Joo
TI - Kernels of Toeplitz operators on the Bergman space
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 4
SP - 1119
EP - 1130
AB - A Coburn theorem says that a nonzero Toeplitz operator on the Hardy space is one-to-one or its adjoint operator is one-to-one. We study the corresponding problem for certain Toeplitz operators on the Bergman space.
LA - eng
KW - Toeplitz operator; Bergman space
UR - http://eudml.org/doc/299427
ER -

References

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  3. Coburn, L. A., 10.1307/mmj/1031732778, Mich. Math. J. 13 (1966), 285-288. (1966) Zbl0173.42904MR0201969DOI10.1307/mmj/1031732778
  4. Guo, K., Zhao, X., Zheng, D., The spectral picture of Bergman Toeplitz operators with harmonic polynomial symbols, Available at https://arxiv.org/abs/2007.07532 (2023), 21 pages. (2023) MR4666991
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  7. Perälä, A., Virtanen, J. A., 10.7153/oam-05-06, Oper. Matrices 5 (2011), 97-106. (2011) Zbl1262.47046MR2798798DOI10.7153/oam-05-06
  8. Sundberg, C., Zheng, D., 10.1512/iumj.2010.59.3799, Indiana Univ. Math. J. 59 (2010), 385-394. (2010) Zbl1195.47019MR2666483DOI10.1512/iumj.2010.59.3799
  9. Vukotić, D., 10.1007/s00020-004-1312-x, Integr. Equations Oper. Theory 50 (2004), 565-567. (2004) Zbl1062.47034MR2105965DOI10.1007/s00020-004-1312-x
  10. Zhu, K., 10.1090/surv/138, Mathematical Surveys and Monographs 138. AMS, Providence (2007). (2007) Zbl1123.47001MR2311536DOI10.1090/surv/138

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