Abstract
The famous von Neumann-Wold Theorem tells us that each analytic Toeplitz operator with n + 1-Blaschke factors is unitary to n + 1 copies of the unilateral shift on the Hardy space. It is obvious that the von Neumann-Wold Theorem does not hold in the Bergman space. In this paper, using the basis constructed by Michael and Zhu on the Bergman space we prove that each analytic Toeplitz operator M B(z) is similar to n + 1 copies of the Bergman shift if and only if B(z) is an n + 1-Blaschke product. From the above theorem, we characterize the similarity invariant of some analytic Toeplitz operators by using K 0-group term.
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This work was supported by the National Natural Science Foundation of China (Grant No. 10571041)
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Jiang, Cl., Li, Yc. The commutant and similarity invariant of analytic Toeplitz operators on Bergman space. SCI CHINA SER A 50, 651–664 (2007). https://doi.org/10.1007/s11425-007-0027-2
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DOI: https://doi.org/10.1007/s11425-007-0027-2