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Invertible weighted composition operators preserve frames on Dirichlet type spaces
oleh: Ruishen Qian, Xiangling Zhu
Format: | Article |
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Diterbitkan: | AIMS Press 2020-05-01 |
Deskripsi
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.