Title: Dvoretzky-type theorem for locally finite subsets of a Hilbert space (joint with S. Ostrovska and M. Ostrovskii)
Speaker: Florin Catrina (St. John’s University, New York)
Speaker's URL: https://www.stjohns.edu/academics/faculty/florin-catrina
Abstract: The main result of the talk: Given any $\epsilon>0$, every locally finite subset of $\ell_2$ admits a $(1+\epsilon)$-bilipschitz embedding into an arbitrary infinite-dimensional Banach space.
The result is based on two results which are of independent interest:
(1) A direct sum of two finite-dimensional Euclidean spaces contains a sub-sum of a controlled dimension which is $\epsilon$-close to a direct sum with respect to a $1$-unconditional basis in a two-dimensional space.
(2) For any finite-dimensional Banach space $Y$ and its direct sum $X$ with itself with respect to a $1$-unconditional basis in a two-dimensional space, there exists a $(1+\epsilon)$-bilipschitz embedding of $Y$ into $X$ which on a small ball coincides with the identity map onto the first summand and on a complement of a large ball coincides with the identity map onto the second summand.
URL associated with Seminar: https://u.osu.edu/aots/
