A Shimorin-type analytic model on an annulus for left-invertible operators and applications
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arXiv
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866913829737201664 |
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| author | Pietrzycki, Pawel |
| author_facet | Pietrzycki, Pawel |
| contents | A new analytic model for left-invertible operators, which extends both Shimorin's analytic model for left-invertible and analytic operators and Gellar's model for bilateral weighted shift is introduced and investigated. We show that a left-invertible operator $T$, which satisfies certain conditions can be modelled as a multiplication operator $\mathscr{M}_z$ on a reproducing kernel Hilbert space of vector-valued analytic functions on an annulus or a disc. A similar result for composition operators in $\ell^2$-spaces is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_03339 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A Shimorin-type analytic model on an annulus for left-invertible operators and applications Pietrzycki, Pawel Functional Analysis Complex Variables Spectral Theory A new analytic model for left-invertible operators, which extends both Shimorin's analytic model for left-invertible and analytic operators and Gellar's model for bilateral weighted shift is introduced and investigated. We show that a left-invertible operator $T$, which satisfies certain conditions can be modelled as a multiplication operator $\mathscr{M}_z$ on a reproducing kernel Hilbert space of vector-valued analytic functions on an annulus or a disc. A similar result for composition operators in $\ell^2$-spaces is established. |
| title | A Shimorin-type analytic model on an annulus for left-invertible operators and applications |
| topic | Functional Analysis Complex Variables Spectral Theory |
| url | https://arxiv.org/abs/1808.03339 |