Commutant lifting, interpolation, and perturbations on the polydisc
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909775047950336 |
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| author | D., Deepak K. Sarkar, Jaydeb |
| author_facet | D., Deepak K. Sarkar, Jaydeb |
| contents | The fundamental theorem on commutant lifting due to Sarason does not carry over to the setting of the polydisc. This paper presents two classifications of commutant lifting in several variables. The first classification links the lifting problem to the contractivity of certain linear functionals. The second one transforms it into nonnegative real numbers via a distance formula. We also solve the Nevanlinna-Pick interpolation problem for bounded analytic functions on the polydisc. Along the way, we solve a perturbation problem for bounded analytic functions. Commutant lifting and interpolation on the polydisc solve two well-known problems in Hilbert function space theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_10020 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Commutant lifting, interpolation, and perturbations on the polydisc D., Deepak K. Sarkar, Jaydeb Functional Analysis Complex Variables Operator Algebras 32A38, 47A57, 30E05, 47A13, 46J15, 30D55, 93C73, 15B05 The fundamental theorem on commutant lifting due to Sarason does not carry over to the setting of the polydisc. This paper presents two classifications of commutant lifting in several variables. The first classification links the lifting problem to the contractivity of certain linear functionals. The second one transforms it into nonnegative real numbers via a distance formula. We also solve the Nevanlinna-Pick interpolation problem for bounded analytic functions on the polydisc. Along the way, we solve a perturbation problem for bounded analytic functions. Commutant lifting and interpolation on the polydisc solve two well-known problems in Hilbert function space theory. |
| title | Commutant lifting, interpolation, and perturbations on the polydisc |
| topic | Functional Analysis Complex Variables Operator Algebras 32A38, 47A57, 30E05, 47A13, 46J15, 30D55, 93C73, 15B05 |
| url | https://arxiv.org/abs/2301.10020 |