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SUMMARY:On Banach’s isometric subspaces problem - Daniil Mamaev\, PDMI R
 AS and LSGNT
DTSTART:20230524T150000Z
DTEND:20230524T160000Z
UID:TALK201628@talks.cam.ac.uk
CONTACT:104686
DESCRIPTION:Is a normed vector space V whose n-dimensional linear subspace
 s are all isometric\, for a fixed 2 <= n < dim V\, necessarily Euclidean? 
 This question was asked in 1932 by S. Banach and in the known cases the an
 swer is always affirmative. In a joint work with S. Ivanov and A. Nordskov
 a we handle `the smallest' previously unresolved case n = 3\, but the prob
 lem remains open for n + 1 = dim V = 4k >= 8 and n + 1= dim V = 134. \n\nI
  will start by formulating the problem in a couple equivalent ways\, then 
 give an overview of previous partial results\, and proceed by sketching th
 e proof in the case n = 3. If time permits\, I will also discuss the local
  (stronger) version of the problem and its application to Finsler geometry
 .  
LOCATION:MR13
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