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Rank-one cross commutators on backward shift invariant subspaces on the bidisk

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Abstract

For a backward shift invariant subspace N in H 2(Γ2), the operators S z and S w on N are defined by S z = P N T z | N and S w = P N T w | N , where P N is the orthogonal projection from L 2(Γ2) onto N. We give a characterization of N satisfying rank [S z , S * w ] = 1.

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Authors and Affiliations

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

    Kei Ji Izuchi

  2. Graduate School of Science and Technology, Niigata University, Niigata, 950-2181, Japan

    Kou Hei Izuchi

  3. Department of Mathematics, Graduate School of Science, Hokkaido University, Sapporo, 060-0810, Japan

    Kou Hei Izuchi

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

Additional information

The first author is partially supported by Grant-in-Aid for Scientific Research (No. 16340037), Japan Society for the Promotion of Science

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Izuchi, K.J., Izuchi, K.H. Rank-one cross commutators on backward shift invariant subspaces on the bidisk. Acta. Math. Sin.-English Ser. 25, 693–714 (2009). https://doi.org/10.1007/s10114-009-7215-7

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  • DOI: https://doi.org/10.1007/s10114-009-7215-7

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