# REDUCING SUBSPACES FOR TOEPLITZ OPERATORS ON THE POLYDISK

• Shi, Yanyue (College of Mathematical Science Ocean University of China) ;
• Lu, Yufeng (School of Mathematical Sciences Dalian University of Technology)
• Published : 2013.03.31
• 126 13

#### Abstract

In this note, we completely characterize the reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on $A^2_{\alpha}(D^2)$ where ${\alpha}$ > -1 and N, M are positive integers with $N{\neq}M$, and show that the minimal reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on the unweighted Bergman space and on the weighted Bergman space are different.

#### Keywords

Toeplitz operator;reducing subspace;Bergman space

#### References

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