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Mixed invariant subspaces over the bidisk II

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Abstract

For a mixed invariant subspace N of H 2 under T z and \(T^{*}_{w}\), in the previous paper we studied the case rank[V z ,V w ]=1 and either dim(N⊖zN)=0 or 1. In this paper, we study the structure of N satisfying rank[V z ,V w ]=1 and dim(N⊖zN)=2. Our study is deeply concerned with the structure of nonextreme points in the closed unit ball of the space of one variable bounded analytic functions.

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Acknowledgements

The first author is partially supported by Grant-in-Aid for Scientific Research (No. 21540166), Japan Society for the Promotion of Science.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Education, Yamaguchi University, Yamaguchi, 753-8511, Japan

    Kou Hei Izuchi

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

    Kei Ji Izuchi

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  1. Kou Hei Izuchi
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  2. Kei Ji Izuchi
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Correspondence to Kei Ji Izuchi.

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Izuchi, K.H., Izuchi, K.J. Mixed invariant subspaces over the bidisk II. Acta Math Vietnam. 38, 213–239 (2013). https://doi.org/10.1007/s40306-013-0016-1

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  • DOI: https://doi.org/10.1007/s40306-013-0016-1

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