Invertible weighted composition operators preserve frames on Dirichlet type spaces
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 e...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2020-05-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020273/fulltext.html |
| Summary: | 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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| ISSN: | 2473-6988 |