Reducing subspaces for a class of Toeplitz operators on the Bergman space of the bidisk
Bull. Korean Math. Soc. 2015 Vol. 52, No. 5, 1649-1660
Printed September 30, 2015
Mohammed Albaseer, Yufeng Lu, and Yanyue Shi
Dalian University of Technology, Dalian University of Technology, Ocean University of China
Abstract : In this paper, we completely characterize the nontrivial reducing subspaces of the Toeplitz operator $T_{z_{1}^{N}\overline{z}_{2}^{M}}$ on the Bergman space $A^{2}(\mathbb{D}^2)$, where $N$ and $M$ are positive integers.
Keywords : reducing subspace, Toeplitz operator, polydisk
MSC numbers : Primary 47B35, 46E22
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