Sharp finiteness principles for Lipschitz selections

Charles Fefferman; Pavel Shvartsman

Sharp finiteness principles for Lipschitz selections

Functional Analysis 2018-08-07 v3

Authors: Charles Fefferman , Pavel Shvartsman

Abstract

Let $(M,\rho)$ be a metric space and let $Y$ be a Banach space. Given a positive integer $m$ , let $F$ be a set-valued mapping from $M$ into the family of all compact convex subsets of $Y$ of dimension at most $m$ . In this paper we prove a finiteness principle for the existence of a Lipschitz selection of $F$ with the sharp value of the finiteness constant.

Keywords

lipschitz spaces fixed point in banach spaces banach spaces

Cite

@article{arxiv.1801.00325,
  title  = {Sharp finiteness principles for Lipschitz selections},
  author = {Charles Fefferman and Pavel Shvartsman},
  journal= {arXiv preprint arXiv:1801.00325},
  year   = {2018}
}

Comments

57 pages. arXiv admin note: substantial text overlap with arXiv:1708.00811

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