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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Transportation cost spaces on finite metric spaces
- Denka Kutzarova (University of Illinois at Urba
na-Champaign\; Bulgarian Academy of Sciences)
DTSTART;TZID=Europe/London:20190617T111000
DTEND;TZID=Europe/London:20190617T120000
UID:TALK126067AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/126067
DESCRIPTION:Transportation cost spaces are studied by several
groups of researchers\, for different reasons and
under different names. The term Lipschitz-free spa
ces is commonly used in Banach space theory.

W
e prove that the transportation cost space on any
finite metric space contains a large well-compleme
nted subspace which is close to $\\ell_1^n$.

We show that transportation cost spaces on large c
lasses of recursively defined sequences of graphs
are not uniformly isomorphic to $\\ell_1^n$ of the
corresponding dimensions. These classes contain w
ell-known families of diamond graphs and Laakso gr
aphs.

In the particular case of diamond graphs
we prove that their cycle space is spanned by eve
n levels of Haar functions. It is curious that the
subspaces generated by all the even/odd levels of
the Haar functions also appear in the study of qu
asi-greedy basic sequences in $L_1[0\,1]$.

Thi
s research is joint with Stephen Dilworth and Mikh
ail Ostrovskii.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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