Invertibility and spectral properties of dual Toeplitz operators
| Autor: | Shengkun Wu, Xianfeng Zhao, Xuanhao Ding |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Mathematics::Functional Analysis
Pure mathematics Mathematics::Operator Algebras Applied Mathematics 010102 general mathematics Spectrum (functional analysis) Orthogonal complement Harmonic (mathematics) 01 natural sciences Toeplitz matrix law.invention 010101 applied mathematics Invertible matrix law Bergman space Bounded function Computer Science::Symbolic Computation 0101 mathematics Analysis Mathematics Toeplitz operator |
| Zdroj: | Journal of Mathematical Analysis and Applications. 484:123762 |
| ISSN: | 0022-247X |
| Popis: | In this paper, we consider dual Toeplitz operators with continuous symbols and bounded harmonic symbols on the orthogonal complement of the Bergman space over the open unit disk. We construct a dual Toeplitz operator with continuous symbol such that its spectrum is disconnected. On the other hand, we show that the spectra of dual Toeplitz operators with certain class of bounded harmonic symbols are connected, which leads to some partial answers to the open question posed by Stroethoff and Zheng [18] in 2002. We obtain a complete characterization for the hyponormality of dual Toeplitz operators with bounded harmonic symbols. Moreover, we establish some sufficient conditions that are convenient to check for dual Toeplitz operators with continuous symbols and bounded harmonic symbols to be invertible, respectively. |
| Databáze: | OpenAIRE |
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