Reducing Subspaces of Toeplitz Operators on Nφ-type Quotient Modules on the Torus

Reducing Subspaces of Toeplitz Operators on Nφ-type Quotient Modules on the Torus

In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol Sψ（z） on Nφ has at least m non-trivial minimal reducing subspaces, where m is the dimension of H^2（Гω）⊙φ（ω）H^2（Гω）. Moreover, the restriction of Sψ（z） on any of these minimal reducing subspaces is unitary equivale...

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Veröffentlicht in:数学研究通讯：英文版 2009, Vol.25 (1), p.19-29
1. Verfasser: WU NAN Xu XIAN-MIN
Format: Artikel
Sprache:eng
Schlagworte:
Toeplitz算子
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Zusammenfassung:In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol Sψ（z） on Nφ has at least m non-trivial minimal reducing subspaces, where m is the dimension of H^2（Гω）⊙φ（ω）H^2（Гω）. Moreover, the restriction of Sψ（z） on any of these minimal reducing subspaces is unitary equivalent to the Bergman shift Mz.
ISSN:1674-5647