Year: 2009
Author: Yan Wu, Xianmin Xu
Communications in Mathematical Research , Vol. 25 (2009), Iss. 1 : pp. 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 $M_z$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-CMR-19071
Communications in Mathematical Research , Vol. 25 (2009), Iss. 1 : pp. 19–29
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: module $N_ϕ$-type quotient module the analytic Toeplitz operator reducing subspace finite Blaschke product