Reducing Subspaces of Toeplitz Operators on $N_ϕ$-Type Quotient Modules on the Torus

Reducing Subspaces of Toeplitz Operators on $N_ϕ$-Type Quotient Modules on the Torus

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

Author Details

Yan Wu

Xianmin Xu