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Lu, Yufeng; Zhou, Xiaoyang

Invariant subspaces and reducing subspaces of weighted Bergman space over bidisk. (English) Zbl 1202.47008

J. Math. Soc. Japan 62, No. 3, 745-765 (2010).
The authors investigate invariant subspaces of Toeplitz operators acting in the weighted Bergman space on the bidisk. They obtain a complete description of minimal reducing subspaces of a Toeplitz operator of the form \(T_{z_{1}^{N}z_{2}^{N}}\), \(N>1\). Moreover, they prove that every \(T_{z_{1}}\)-invariant subspace \(M\) is generated by \(M\ominus T_{z_{1}}M\).
Reviewer: Vladimir S. Pilidi (Rostov-na-Donu)

Cited in 18 Documents

MSC:

47A15 Invariant subspaces of linear operators
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
32A36 Bergman spaces of functions in several complex variables

Keywords:

weighted Bergman space; bidisk; invariant subspace; reducing subspace
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\textit{Y. Lu} and \textit{X. Zhou}, J. Math. Soc. Japan 62, No. 3, 745--765 (2010; Zbl 1202.47008)
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