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Wandering subspaces and the Beurling type Theorem I

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Abstract

An elementary proof of the Aleman, Richter and Sundberg theorem concerning the invariant subspaces of the Bergman space is given.

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References

  1. Aleman A., Richter S., Sundberg C.: Beurling’s theorem for the Bergman space. Acta Math. 117, 275–310 (1996)

    Article  MathSciNet  Google Scholar 

  2. Apostol C. et al.: Invariant subspaces, dilation theory, and the structure of the predual of a dual algebra. I, J. Funct. Anal. 63, 369–404 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  3. Beurling A.: On two problems concerning linear transformations in Hilbert space. Acta Math. 81, 239–255 (1949)

    Article  Google Scholar 

  4. P. Duren and A. Schuster, Bergman Spaces, Mathematical Surveys and Monographs, 100, American Mathematical Society, Providence, RI, 2004.

  5. Hedenmalm H.: An invariant subspace of the Bergman space having the codimension two property. J. reine angew. Math. 443, 1–9 (1993)

    MATH  MathSciNet  Google Scholar 

  6. Hedenmalm H., Korenblum B., Zhu K.: Theory of Bergman Spaces, Graduate Texts in Mathematics, 199. Springer-Verlag, New York (2000)

    Google Scholar 

  7. Hedenmalm H., Richter S., Seip K.: Interpolating sequences and invariant subspaces of given index in the Bergman spaces. J. reine angew. Math. 477, 13–30 (1996)

    MATH  MathSciNet  Google Scholar 

  8. McCullough S., Richter S.: Bergman-type reproducing kernels, contractive divisors, and dilations. J. Funct. Anal. 190, 447–480 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Olofsson A.: Wandering subspace theorems. Integr. Eq. Op. Theory 51, 395–409 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Shimorin S.: Wold-type decompositions and wandering subspaces for operators close to isometries. J. reine angew. Math. 531, 147–189 (2001)

    MATH  MathSciNet  Google Scholar 

  11. Sun S., Zheng D.: Beurling type theorem on the Bergman space via the Hardy space of the bidisk. Sci. China Ser. A 52, 2517–2529 (2009)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Niigata University, Niigata, 950-2181, Japan

    Kei Ji Izuchi

  2. Institute of Basic Science, Korea University, Seoul, 136-713, Republic of Korea

    Kou Hei Izuchi

  3. Aoyama-shinmachi 18-6-301, Niigata, 950-2006, Japan

    Yuko Izuchi

Authors
  1. Kei Ji Izuchi
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  2. Kou Hei Izuchi
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  3. Yuko Izuchi
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Correspondence to Kou Hei Izuchi.

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Izuchi, K.J., Izuchi, K.H. & Izuchi, Y. Wandering subspaces and the Beurling type Theorem I. Arch. Math. 95, 439–446 (2010). https://doi.org/10.1007/s00013-010-0178-1

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  • DOI: https://doi.org/10.1007/s00013-010-0178-1

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