Duality for Lipschitz p-summing operators
Duration: 51 mins 59 secs
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| Description: |
Chavez-Dominguez, JA (Texas A&M)
Monday 10 January 2011, 16:30-17:30 |
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| Created: | 2011-01-11 10:11 | ||||
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| Collection: | Discrete Analysis | ||||
| Publisher: | Isaac Newton Institute | ||||
| Copyright: | Chavez-Dominguez, JA | ||||
| Language: | eng (English) | ||||
| Distribution: |
World
(downloadable)
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| Explicit content: | No | ||||
| Aspect Ratio: | 16:9 | ||||
| Screencast: | No | ||||
| Bumper: | UCS Default | ||||
| Trailer: | UCS Default | ||||
| Abstract: | A theorem of J. Bourgain states that any finite metric space can be embedded into a Hilbert space with distortion proportional to the logarithm of the number of points. In fact Bourgain's embedding has a richer structure, that of a Lipschitz p-summing operator. These operators were introduced by J. Farmer and W. B. Johnson, and generalize the concept of a linear p-summing operator between Banach spaces . In this talk we identify the dual of the space of Lipschitz p-summing operators from a fi nite metric space to a normed space, answering a question of Farmer and Johnson. Furthermore, we use it to give a characterization of the non-linear concept of Lipschitz p-summing operator between metric spaces in terms of linear operators between certain Banach spaces. |
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