This is an announcement for the paper “Linear properties of Banach spaces and low distortion embeddings of metric graphs” by Antonin Prochazka.

Abstract: We characterize non-reflexive Banach spaces by a low-distortion (resp. isometric) embeddability of a certain metric graph up to a renorming. Also we study non-linear sufficient conditions for $\ell_1^n$ being $1+\epsilon$-isomorphic to a subspace of a Banach space $X$.

The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.00741