Schwarz-Pick type inequalities from an operator theoretical point of view
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911960244682752 |
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| author | Badea, Catalin Renard, Axel |
| author_facet | Badea, Catalin Renard, Axel |
| contents | We use (versions of) the von Neumann inequality for Hilbert space contractions to prove several Schwarz-Pick inequalities. Specifically, we derive an alternate proof for a multi-point Schwarz-Pick inequality by Beardon and Minda, along with a generalized version for operators. Connections with model spaces and Peschl's invariant derivatives are established. Finally, Schwarz-Pick inequalities for analytic functions on polydisks and for higher order derivatives are discussed. An enhanced version of the Schwarz-Pick lemma, using the notion of distinguished variety, is obtained for the bidisk. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01357 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Schwarz-Pick type inequalities from an operator theoretical point of view Badea, Catalin Renard, Axel Functional Analysis Complex Variables Spectral Theory 47A25, 47A30, 47A08, 30A10, 30C80, 15A60 We use (versions of) the von Neumann inequality for Hilbert space contractions to prove several Schwarz-Pick inequalities. Specifically, we derive an alternate proof for a multi-point Schwarz-Pick inequality by Beardon and Minda, along with a generalized version for operators. Connections with model spaces and Peschl's invariant derivatives are established. Finally, Schwarz-Pick inequalities for analytic functions on polydisks and for higher order derivatives are discussed. An enhanced version of the Schwarz-Pick lemma, using the notion of distinguished variety, is obtained for the bidisk. |
| title | Schwarz-Pick type inequalities from an operator theoretical point of view |
| topic | Functional Analysis Complex Variables Spectral Theory 47A25, 47A30, 47A08, 30A10, 30C80, 15A60 |
| url | https://arxiv.org/abs/2405.01357 |