On Schauder basis in normed spaces

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. As applications of these results, we show the Principle of Selection of Bessaga-Pe\l{}czy\'nski for normed spaces and the Spectral Theorem for compact self-adjoint operators on inner product spaces.Comment: 15 pages. Improvement of the paper, including a Spectral Theorem in this contex