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Aϕ-Invariant Subspaces on the Torus

Published online by Cambridge University Press:  20 November 2018

Keiji Izuchi  and
Yasuo Matsugu
Keiji Izuchi
Affiliation:
Department of Mathematics Niigata University Niigata950-21 Japan, e-mail: [email protected]
Yasuo Matsugu
Affiliation:
Department of Mathematics Shinshu University Matsumoto 390 Japan, e-mail: [email protected]
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Abstract

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Generalizing the notion of invariant subspaces on the 2-dimensional torus ${{T}^{2}}$, we study the structure of ${{A}_{\phi }}$-invariant subspaces of ${{L}^{2}}({{T}^{2}})$. A complete description is given of ${{A}_{\phi }}$-invariant subspaces that satisfy conditions similar to those studied by Mandrekar, Nakazi, and Takahashi.

Keywords

32A3547A15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 1 , 01 February 1998 , pp. 99 - 133
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Agrawal, O., Clark, D., and Douglas, R., Invariant subspaces in the polydisk. Pacific J. Math. 121 (1986), 1–11.Google Scholar
2. Curto, R., Muhly, P., Nakazi, T., and Yamamoto, T., On superalgebras of the polydisc algebra. Acta Sci. Math. 51 (1987), 413–421.Google Scholar
3. Ghatage, P. and Mandrekar, V., On Beurling type invariant subspaces of L2 (T2) and their equivalence. J. Operator Theory 20 (1988), 83–89.Google Scholar
4. Helson, H. and Lowdenslager, D., Prediction theory and Fourier series in several variables. Acta Math. 99 (1958), 165–202.Google Scholar
5. Hoffman, K., Banach Spaces of Analytic Functions.Prentice-Hall, New Jersey, 1962.Google Scholar
6. Izuchi, K., Unitary equivalence of invariant subspaces in the polydisk. Pacific J. Math. 130 (1987), 351–358.Google Scholar
7. Izuchi, K. and Matsugu, Y., Outer functions and invariant subspaces on the torus. Acta Sci. Math. 59 (1994), 429–440.Google Scholar
8. Izuchi, K. and S.Ohno, Selfadjoint commutators and invariant subspaces on the torus. J.Operator Theory 31 (1994), 189–204.Google Scholar
9. Mandrekar, V., The validity of Beurling theorems in polydiscs. Proc. Amer. Math. Soc. 103 (1988), 145–148.Google Scholar
10. Nakazi, T., Certain invariant subspaces of H2 and L2 on a bidisc. Canad. J.Math. 40 (1988), 1272–1280.Google Scholar
11. Nakazi, T., Homogeneous polynomials and invariant subspaces in the polydisc. Arch. Math. 58 (1992), 56–63.Google Scholar
12. Nakazi, T., Invariant subspaces in the bidisc and commutators. J. Austr. Math. Soc. (Ser. A) 56 (1994), 232–242.Google Scholar
13. Nakazi, T. and Takahashi, K., Homogeneous polynomials and invariant subspaces in the polydisc II. Proc. Amer.Math. Soc. 113 (1991), 991–997.Google Scholar
14. Rudin, W., Function Theory in Polydiscs.Benjamin, New York, 1969.Google Scholar
15. Rudin, W., Invariant subspaces of H2 on a torus. J. Funct. Anal. 61 (1985), 378–384.Google Scholar