Volume 25, Issue 1
Reducing Subspaces of Toeplitz Operators on $N_ϕ$-Type Quotient Modules on the Torus

Commun. Math. Res., 25 (2009), pp. 19-29.

Published online: 2021-05

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• Abstract

In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol $S_{ψ(z)}$ on $N_ϕ$ has at least $m$ non-trivial minimal reducing subspaces, where $m$ is the dimension of $H^2(Γ_ω) ⊖ ϕ(ω)H^2 (Γ_ω)$. Moreover, the restriction of $S_{ψ(z)}$ on any of these minimal reducing subspaces is unitary equivalent to the Bergman shift $M_z$.

• Keywords

module, $N_ϕ$-type quotient module, the analytic Toeplitz operator, reducing subspace, finite Blaschke product

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COPYRIGHT: © Global Science Press

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@Article{CMR-25-19, author = {Yan and Wu and and 18100 and and Yan Wu and Xianmin and Xu and and 18101 and and Xianmin Xu}, title = {Reducing Subspaces of Toeplitz Operators on $N_ϕ$-Type Quotient Modules on the Torus}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {1}, pages = {19--29}, abstract = {

In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol $S_{ψ(z)}$ on $N_ϕ$ has at least $m$ non-trivial minimal reducing subspaces, where $m$ is the dimension of $H^2(Γ_ω) ⊖ ϕ(ω)H^2 (Γ_ω)$. Moreover, the restriction of $S_{ψ(z)}$ on any of these minimal reducing subspaces is unitary equivalent to the Bergman shift $M_z$.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19071.html} }
TY - JOUR T1 - Reducing Subspaces of Toeplitz Operators on $N_ϕ$-Type Quotient Modules on the Torus AU - Wu , Yan AU - Xu , Xianmin JO - Communications in Mathematical Research VL - 1 SP - 19 EP - 29 PY - 2021 DA - 2021/05 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19071.html KW - module, $N_ϕ$-type quotient module, the analytic Toeplitz operator, reducing subspace, finite Blaschke product AB -

In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol $S_{ψ(z)}$ on $N_ϕ$ has at least $m$ non-trivial minimal reducing subspaces, where $m$ is the dimension of $H^2(Γ_ω) ⊖ ϕ(ω)H^2 (Γ_ω)$. Moreover, the restriction of $S_{ψ(z)}$ on any of these minimal reducing subspaces is unitary equivalent to the Bergman shift $M_z$.

Yan Wu & XianminXu. (2021). Reducing Subspaces of Toeplitz Operators on $N_ϕ$-Type Quotient Modules on the Torus. Communications in Mathematical Research . 25 (1). 19-29. doi:
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