Timeline for Continuous automorphism groups of normed vector spaces?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| Feb 3, 2010 at 12:12 | history | edited | Konrad Swanepoel | CC BY-SA 2.5 |
Improvement in light of comments.
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| Feb 1, 2010 at 19:00 | comment | added | Konrad Swanepoel | Could somebody give a good description of the closed subgroups of $O(n)$? Perhaps this deserves to be a new question. In the two-dimensional case, the group is either finite (and dihedral) or the whole $O(2)$. For general $n$, perhaps there is an orthogonal decomposition of the space such that the orbit of a unit vector in each component is either finite or the whole unit sphere. | |
| Feb 1, 2010 at 18:29 | comment | added | Jason Reed | Sorry, I may have misunderstood the norms of what "accepting" an answer is supposed to mean. | |
| Feb 1, 2010 at 16:53 | comment | added | Bill Johnson | Why was this answer accepted? Konrad suggested an approach but did not give an answer. | |
| Feb 1, 2010 at 15:54 | comment | added | Bill Johnson | There is no problem making the unit ball full dimensional, since you can include the orbit under $G$ of the unit vector basis. This is no loss of generality by Auerbach's lemma. Also, this construction, if it works would give a unit ball that is inside the Euclidean ball. The Euclidean ball would be the ellipsoid of minimal volume containing the unit ball (i.e., the polar of the John ellipsoid). | |
| Feb 1, 2010 at 14:50 | vote | accept | Jason Reed | ||
| Feb 1, 2010 at 18:22 | |||||
| Feb 1, 2010 at 14:47 | vote | accept | Jason Reed | ||
| Feb 1, 2010 at 14:50 | |||||
| Feb 1, 2010 at 13:23 | history | edited | Konrad Swanepoel | CC BY-SA 2.5 |
Added requirement that an isometry fixes the origin.
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| Feb 1, 2010 at 6:50 | history | edited | Konrad Swanepoel | CC BY-SA 2.5 |
Added introductory sentence explaining the relation to the question.
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| Feb 1, 2010 at 0:31 | history | answered | Konrad Swanepoel | CC BY-SA 2.5 |