Reducing subspaces for a class of non-analytic Toeplitz operators on the bidisk

In this paper, we completely characterize all the reducing subspaces for a class of non-analytic Toeplitz operators with symbol φ(z,w)=αzk+βw‾l, where α,β∈C and αβ≠0. We also prove that the von Neumann algebra V⁎(φ)={Tφ,Tφ⁎}′ is abelian.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2017-01, Vol.445 (1), p.784-796
Main Authors: Deng, Jia, Lu, Yufeng, Shi, Yanyue
Format: Article
Language:English
Subjects:
Bergman space
Polydisk
Reducing subspace
Toeplitz operator
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Summary:In this paper, we completely characterize all the reducing subspaces for a class of non-analytic Toeplitz operators with symbol φ(z,w)=αzk+βw‾l, where α,β∈C and αβ≠0. We also prove that the von Neumann algebra V⁎(φ)={Tφ,Tφ⁎}′ is abelian.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2016.08.012