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SUMMARY:Transportation cost spaces on finite metric spaces - Denka Kutzaro
 va (University of Illinois at Urbana-Champaign\; Bulgarian Academy of Scie
 nces)
DTSTART:20190617T101000Z
DTEND:20190617T110000Z
UID:TALK126067@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Transportation cost spaces are studied by several groups of re
 searchers\, for different reasons and under different names. The term Lips
 chitz-free spaces is commonly used in Banach space theory.<br> We prove th
 at the transportation cost space on any finite metric space contains a lar
 ge well-complemented subspace which is close to $\\ell_1^n$. <br> We show 
 that transportation cost spaces on large classes of recursively defined se
 quences of graphs are not uniformly isomorphic to $\\ell_1^n$ of the corre
 sponding dimensions. These classes contain well-known families of diamond 
 graphs and Laakso graphs.<br> In the particular case of diamond graphs we 
 prove that their cycle space is spanned by even levels of Haar functions. 
 It is curious that the subspaces generated by all the even/odd levels of t
 he Haar functions also appear in the study of quasi-greedy basic sequences
  in $L_1[0\,1]$.<br> This research is joint with Stephen Dilworth and Mikh
 ail Ostrovskii.
LOCATION:Seminar Room 1\, Newton Institute
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