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

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 \(M\ominus T_{z_{1}}M\).


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