Abstract
It is known that Rudin constructed an infinitely generated submodule in the Hardy space over the bidisk. In this paper, we give a new proof that Rudin’s module is not finitely generated.
This research was supported by the Grant-in-Aid for Scientific Research, Japan Society for Promotion of Science.
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References
R. G. Douglas and R. Yang, Operator theory in the Hardy space over the bidisk (I), Integr. equ. oper. theory 38 (2000), 207–221.
W. Rudin, Function theory in polydiscs, Benjamin, New York, 1969.
M. Seto, Infinite sequences of inner functions and submodules in H 2(\( \mathbb{D} \) 2), to appear in J. operator theory.
M. Seto and R. Yang, Inner sequence based invariant subspaces in H 2(\( \mathbb{D} \) 2), Proc. Amer. Math. Soc. 135 (2007), 2519–2526.
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© 2008 Birkhäuser Verlag Basel/Switzerland
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Seto, M. (2008). A New Proof that Rudin’s Module is not Finitely Generated. In: Ando, T., Curto, R.E., Jung, I.B., Lee, W.Y. (eds) Recent Advances in Operator Theory and Applications. Operator Theory: Advances and Applications, vol 187. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8893-5_12
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DOI: https://doi.org/10.1007/978-3-7643-8893-5_12
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