Every separable Banach space has a bounded strong norming biorthogonal sequence which is also a Steinitz basis
Studia Mathematica, Tome 111 (1994) no. 3, pp. 207-222
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $x ∈ \overline{conv} {finite subseries of ∑_{n=1}^{∞} z*_n(x)z_n} and x*_n(x) = ∑_{n=1}^∞ z*_{π(n)}(x)x*(z_{π(n)})$.
@article{10_4064_sm_111_3_207_222,
author = {Paolo Terenzi},
title = {Every separable {Banach} space has a bounded strong norming biorthogonal sequence which is also a {Steinitz} basis},
journal = {Studia Mathematica},
pages = {207--222},
publisher = {mathdoc},
volume = {111},
number = {3},
year = {1994},
doi = {10.4064/sm-111-3-207-222},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-111-3-207-222/}
}
TY - JOUR AU - Paolo Terenzi TI - Every separable Banach space has a bounded strong norming biorthogonal sequence which is also a Steinitz basis JO - Studia Mathematica PY - 1994 SP - 207 EP - 222 VL - 111 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-111-3-207-222/ DO - 10.4064/sm-111-3-207-222 LA - en ID - 10_4064_sm_111_3_207_222 ER -
%0 Journal Article %A Paolo Terenzi %T Every separable Banach space has a bounded strong norming biorthogonal sequence which is also a Steinitz basis %J Studia Mathematica %D 1994 %P 207-222 %V 111 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-111-3-207-222/ %R 10.4064/sm-111-3-207-222 %G en %F 10_4064_sm_111_3_207_222
Paolo Terenzi. Every separable Banach space has a bounded strong norming biorthogonal sequence which is also a Steinitz basis. Studia Mathematica, Tome 111 (1994) no. 3, pp. 207-222. doi: 10.4064/sm-111-3-207-222
Cité par Sources :