Every separable Banach space has a bounded strong norming biorthogonal sequence which is also a Steinitz basis
Volume 111 / 1994
Studia Mathematica 111 (1994), 207-222
DOI: 10.4064/sm-111-3-207-222
Abstract
Every separable, infinite-dimensional Banach space X has a biorthogonal sequence ${z_n, z*_n}$, with $span{z*_n}$ norming on X and ${∥z_n∥ + ∥z*_n∥}$ bounded, so that, for every x in X and x* in X*, there exists a permutation {π(n)} of {n} so that $x ∈ \overline{conv} {finite subseries of ∑_{n=1}^{∞} z*_n(x)z_n} and x*_n(x) = ∑_{n=1}^∞ z*_{π(n)}(x)x*(z_{π(n)})$.
