Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(2): 687-696

Printed March 31, 2013

https://doi.org/10.4134/BKMS.2013.50.2.687

Copyright © The Korean Mathematical Society.

Reducing subspaces for Toeplitz operators on the polydisk

Yanyue Shi and Yufeng Lu

Ocean University of China, Dalian University of Technology

Abstract

In this note, we completely characterize the reducing subspaces of $T_{z_1^Nz_2^M}$ on $A_{\alpha}^{2}(D^{2})$ where $\alpha>-1$ and $N,M$ are positive integers with $N\neq M$, and show that the minimal reducing subspaces of $T_{z_1^Nz_2^M}$ on the unweighted Bergman space and on the weighted Bergman space are different.

Keywords: Toeplitz operator, reducing subspace, Bergman space

MSC numbers: Primary 47B35, 47B38