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Selfadjoint commutators and invariant subspaces on the torus II

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Abstract

In a previous paper, the authors determined the invariant subspaces ofL 2(T 2) on which a certain commutator is selfadjoint. In this paper, we give its generalization.

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References

  1. R. Curto, P. Muhly, T. Nakazi, and T. Yamamoto, On superalgebras of the polydisc algebra, Acta Sci. Math.51(1987), 413–421.

    Google Scholar 

  2. P. Ghatage and V. Mandrekar, On Beurling type invariant subspaces ofL 2(T 2) and their equivalence, J. Operator Theory20(1988), 83–89.

    Google Scholar 

  3. K. Izuchi, Unitarily equivalence of invariant subspaces in the polydisk, Pacific J. Math.130(1987), 351–358.

    Google Scholar 

  4. K. Izuchi and Y. Matsugu, Outer functions and invariant subspaces on the torus, Acta Sci. Math.59(1994), 429–440.

    Google Scholar 

  5. K. Izuchi and S. Ohno, Selfadjoint commutators and invariant subspaces on the torus, J. Operator Theory31(1994), 189–204.

    Google Scholar 

  6. V. Mandrekar, The validity of Beurling theorems in polydiscs, Proc. Amer. Math. Soc.103(1988), 145–148.

    Google Scholar 

  7. T. Nakazi, Certain invariant subspaces ofH 2 andL 2 on a bidisc, Canad. J. Math.40(1988), 1272–1280.

    Google Scholar 

  8. T. Nakazi, Homogeneous polynomials and invariant subspaces in the polydisc, Arch. Math.58(1992), 56–63.

    Google Scholar 

  9. T. Nakazi, Invariant subspaces in the bidisc and commutators, J. Austral. Math. Soc. (Ser. A)56(1994), 232–242.

    Google Scholar 

  10. T. Nakazi and K. Takahashi, Homogeneous polynomials and invariant subspaces in the polydisc II, Proc. Amer Math. Soc.113(1991), 991–997.

    Google Scholar 

  11. N. K. Nikol'ski i, Treatise on the shift operator, Springer-Verlag, Berlin Heidelberg New York Tokyo, 1986.

    Google Scholar 

  12. M. Rosenblum and J. Rovnyak, Hardy classes and operator theory, Oxford University Press, New York, 1985.

    Google Scholar 

  13. W. Rudin, Function theory in polydiscs, Benjamin, New York, 1969.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics Faculty of Science, Niigata University, 950-21, Niigata, Japan

    Keiji Izuchi & Shûichi Ohno

  2. Nippon Institute of Technology, Gakuendai, Miyashiro, Minami-Saitama 345, Japan

    Keiji Izuchi & Shûichi Ohno

Authors
  1. Keiji Izuchi
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  2. Shûichi Ohno
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Dedicated to Professor Kazuyuki Tsurumi on his sixtieth birthday

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Izuchi, K., Ohno, S. Selfadjoint commutators and invariant subspaces on the torus II. Integr equ oper theory 27, 208–220 (1997). https://doi.org/10.1007/BF01191533

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  • DOI: https://doi.org/10.1007/BF01191533

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