Research article

Invertible weighted composition operators preserve frames on Dirichlet type spaces

  • Received: 11 February 2020 Accepted: 30 April 2020 Published: 08 May 2020
  • MSC : 30H99, 47B33

  • Some characterizations for weighted composition operators to be invertible on Dirichlet type spaces $\mathfrak{D}_{\rho}$ are given in this paper when $\rho$ is finite lower type greater than $0$ and upper type less than $1$. In particular, the equivalence between invertible and preserve frames is established. Moreover, weighted composition operators that preserve tight frames and normalized tight frames on the Dirichlet type space $\mathfrak{D}_{\alpha}$ $(0 < \alpha < 1)$ are also investigated.

    Citation: Ruishen Qian, Xiangling Zhu. Invertible weighted composition operators preserve frames on Dirichlet type spaces[J]. AIMS Mathematics, 2020, 5(5): 4285-4296. doi: 10.3934/math.2020273

    Related Papers:

  • Some characterizations for weighted composition operators to be invertible on Dirichlet type spaces $\mathfrak{D}_{\rho}$ are given in this paper when $\rho$ is finite lower type greater than $0$ and upper type less than $1$. In particular, the equivalence between invertible and preserve frames is established. Moreover, weighted composition operators that preserve tight frames and normalized tight frames on the Dirichlet type space $\mathfrak{D}_{\alpha}$ $(0 < \alpha < 1)$ are also investigated.


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