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On the isometric hypothesis of Banach Montejano, Luis
Description
The following is known as the geometric hypothesis of Banach: let V be an m-dimensional Banach space with unit ball B and suppose all n-dimensional subspaces of V are isometric (all the n-sections of B are affinely equivalent). In 1932, Banach conjectured that under this hypothesis V is a Hilbert space (the boundary of B is an ellipsoid). Gromow proved in 1967 that the conjecture is true for n=even and Dvoretzky derived the same conclusion under the hypothesis n=infinity. We prove this conjecture for all positive integers of the form n=4k+1, with the possible exception of 133. The ingredients of the proof are classical homotopic theory, irreducible representations of the orthogonal group and convex geometry
Item Metadata
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On the isometric hypothesis of Banach
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-10-10T15:16
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Description |
The following is known as the geometric hypothesis of Banach: let V be an m-dimensional Banach space with unit ball B and suppose all n-dimensional subspaces of V are isometric (all the n-sections of B are affinely equivalent). In 1932, Banach conjectured that under this hypothesis V is a Hilbert space (the boundary of B is an ellipsoid). Gromow proved in 1967 that the conjecture is true for n=even and Dvoretzky derived the same conclusion under the hypothesis n=infinity. We prove this conjecture for all positive integers of the form n=4k+1, with the possible exception of 133.
The ingredients of the proof are classical homotopic theory, irreducible representations of the orthogonal group and convex geometry
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Extent |
34.0 minutes
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Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Universidad Nacional Autónoma de Mexico
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Series | |
Date Available |
2021-01-13
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0395566
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International