This is an announcement for the paper “On Schauder basis in normed spaces” by Vinicius Coelhohttps://arxiv.org/search/math?searchtype=author&query=Coelho%2C+V, Joilson Ribeirohttps://arxiv.org/search/math?searchtype=author&query=Ribeiro%2C+J, Luciana Salgadohttps://arxiv.org/search/math?searchtype=author&query=Salgado%2C+L.

Abstract: In this work, we prove the criterion of Banach-Grunblum and the principle of selection of Bessaga-Pe\l{}czy'nski for normed spaces. Given these results, it can be shown that in infinite dimension spaces (not necessarily complete) there is an infinite-dimension subspaces with an essential Schauder basis.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1806.07943