Reducing subspaces of Toeplitz operators on Dirichlet type spaces of the bidisk

Hongzhao Lin; Zhongming Teng

Czechoslovak Mathematical Journal (2021)

  • Issue: 1, page 1-19
  • ISSN: 0011-4642

Abstract

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The reducing subspaces of Toeplitz operators T z 1 N z ¯ 2 M on Dirichlet type spaces of the 𝒟 α ( 𝔻 2 ) are described, which extends the results for the corresponding operators on Bergman spaces of the bidisk.

How to cite

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Lin, Hongzhao, and Teng, Zhongming. "Reducing subspaces of Toeplitz operators on Dirichlet type spaces of the bidisk." Czechoslovak Mathematical Journal (2021): 1-19. <http://eudml.org/doc/297316>.

@article{Lin2021,
abstract = {The reducing subspaces of Toeplitz operators $T_\{z_1^N\bar\{z\}_2^M\}$ on Dirichlet type spaces of the $\{\mathcal \{D\}\}_\alpha (\{\mathbb \{D\}\}^2)$ are described, which extends the results for the corresponding operators on Bergman spaces of the bidisk.},
author = {Lin, Hongzhao, Teng, Zhongming},
journal = {Czechoslovak Mathematical Journal},
keywords = {reducing subspace; Toeplitz operator; Dirichlet type space; bidisk},
language = {eng},
number = {1},
pages = {1-19},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Reducing subspaces of Toeplitz operators on Dirichlet type spaces of the bidisk},
url = {http://eudml.org/doc/297316},
year = {2021},
}

TY - JOUR
AU - Lin, Hongzhao
AU - Teng, Zhongming
TI - Reducing subspaces of Toeplitz operators on Dirichlet type spaces of the bidisk
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 1
EP - 19
AB - The reducing subspaces of Toeplitz operators $T_{z_1^N\bar{z}_2^M}$ on Dirichlet type spaces of the ${\mathcal {D}}_\alpha ({\mathbb {D}}^2)$ are described, which extends the results for the corresponding operators on Bergman spaces of the bidisk.
LA - eng
KW - reducing subspace; Toeplitz operator; Dirichlet type space; bidisk
UR - http://eudml.org/doc/297316
ER -

References

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  9. Shi, Y., Lu, Y., 10.4134/BKMS.2013.50.2.687, Bull. Korean Math. Soc. 50 (2013), 687-696. (2013) Zbl1280.47039MR3137713DOI10.4134/BKMS.2013.50.2.687
  10. Stessin, M., Zhu, K., 10.1090/S0002-9939-02-06382-7, Proc. Am. Math. Soc. 130 (2002), 2631-2639. (2002) Zbl1035.47015MR1900871DOI10.1090/S0002-9939-02-06382-7
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