A generalization of Lipschitz mappings
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913633835941888 |
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| author | Karn, Anil Kumar Mandal, Arindam |
| author_facet | Karn, Anil Kumar Mandal, Arindam |
| contents | Using the notion of modulus of continuity at a point of a mapping between metric spaces, we introduce the notion of extensively bounded mappings generalizing that of Lipschitz mappings. We also introduce a metric on it which becomes a norm if the codomain is a normed linear space. We study its basic properties. We also discuss a linearization of an extensively bounded mapping into a bounded linear mapping. As an application, we introduce the notion of extensively bounded operator ideals. We also discuss extensively bounded finite rank and extensively bounded compact mappings and their corresponding operator ideals. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_10677 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A generalization of Lipschitz mappings Karn, Anil Kumar Mandal, Arindam Functional Analysis Primary 46B20, Secondary 46B28 Using the notion of modulus of continuity at a point of a mapping between metric spaces, we introduce the notion of extensively bounded mappings generalizing that of Lipschitz mappings. We also introduce a metric on it which becomes a norm if the codomain is a normed linear space. We study its basic properties. We also discuss a linearization of an extensively bounded mapping into a bounded linear mapping. As an application, we introduce the notion of extensively bounded operator ideals. We also discuss extensively bounded finite rank and extensively bounded compact mappings and their corresponding operator ideals. |
| title | A generalization of Lipschitz mappings |
| topic | Functional Analysis Primary 46B20, Secondary 46B28 |
| url | https://arxiv.org/abs/2410.10677 |