Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON SIMILARITY AND REDUCING SUBSPACES OF A CLASS OF OPERATOR ON THE DIRICHLET SPACE

  • Caixing Gu (Department of Mathematics California Polytechnic State University) ;
  • Yucheng Li (Department of Mathematics Hebei Province Key Laboratory of Computational Mathematics and Applications Hebei Normal University) ;
  • Hexin Zhang (Department of Mathematics Hebei Normal University)
  • Received : 2023.09.01
  • Accepted : 2024.02.06
  • Published : 2024.07.31
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Abstract

Let Yp be the multiplication operator Mp plus the Volterra operator Vp induced by p(z), where p is a polynomial. Under a mild condition, we prove that Yp acting on the Dirichlet space 𝔇 is similar to multiplication operator Mp acting on a subspace S(𝔻) of 𝔇. Furthermore, it shows that Tzn (n ≥ 2) has exactly 2n reducing subspaces on 𝔇.

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Acknowledgement

The authors would like to thank the reviewers for their helpful comments and suggestions which improved the manuscript.

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