Reducing Subspaces of Toeplitz Operators on $N_ϕ$-Type Quotient Modules on the Torus
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@Article{CMR-25-19,
author = {Wu , Yan and Xu , Xianmin},
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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