Aluthge transforms of unbounded weighted composition operators in $L^2$-spaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866915034119012352 |
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| author | Benhida, Chafiq Budzynski, Piotr Trepkowski, Jacek |
| author_facet | Benhida, Chafiq Budzynski, Piotr Trepkowski, Jacek |
| contents | We describe the Aluthge transform of an unbounded weighted composition operator acting in an $L^2$-space. We show that its closure is also a weighted composition operator with the same symbol and a modified weight function. We investigate its dense definiteness. We characterize $p$-hyponormality of unbounded weighted composition operators and provide results on how it is affected by the Aluthge transformation. We show that the only fixed points of the Aluthge transformation on weighted composition operators are quasinormal ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_01205 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Aluthge transforms of unbounded weighted composition operators in $L^2$-spaces Benhida, Chafiq Budzynski, Piotr Trepkowski, Jacek Functional Analysis Primary 47B38, 47B37, 47B33, 47B20, secondary 47B49 We describe the Aluthge transform of an unbounded weighted composition operator acting in an $L^2$-space. We show that its closure is also a weighted composition operator with the same symbol and a modified weight function. We investigate its dense definiteness. We characterize $p$-hyponormality of unbounded weighted composition operators and provide results on how it is affected by the Aluthge transformation. We show that the only fixed points of the Aluthge transformation on weighted composition operators are quasinormal ones. |
| title | Aluthge transforms of unbounded weighted composition operators in $L^2$-spaces |
| topic | Functional Analysis Primary 47B38, 47B37, 47B33, 47B20, secondary 47B49 |
| url | https://arxiv.org/abs/1809.01205 |