The complemented subspace problem revisited
Studia Mathematica, Tome 188 (2008) no. 3, pp. 223-257
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We show that if $X$ is an infinite-dimensional
Banach space in which every finite-dimensional subspace is
$\lambda$-complemented with $\lambda\le 2$ then $X$ is
$(1+C\sqrt{\lambda-1})$-isomorphic to a Hilbert space, where $C$
is an absolute constant; this estimate (up to the constant $C$) is
best possible. This answers a question of Kadets and Mityagin
from 1973. We also investigate the finite-dimensional versions of
the theorem.
Keywords:
infinite dimensional banach space which every finite dimensional subspace lambda complemented lambda sqrt lambda isomorphic hilbert space where absolute constant estimate constant best possible answers question kadets mityagin investigate finite dimensional versions theorem
Affiliations des auteurs :
N. J. Kalton 1
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author = {N. J. Kalton},
title = {The complemented subspace problem revisited},
journal = {Studia Mathematica},
pages = {223--257},
publisher = {mathdoc},
volume = {188},
number = {3},
year = {2008},
doi = {10.4064/sm188-3-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm188-3-2/}
}
N. J. Kalton. The complemented subspace problem revisited. Studia Mathematica, Tome 188 (2008) no. 3, pp. 223-257. doi: 10.4064/sm188-3-2
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