The complemented subspace problem revisited

N. J. Kalton. "The complemented subspace problem revisited." Studia Mathematica 188.3 (2008): 223-257. <http://eudml.org/doc/284930>.

@article{N2008,
abstract = {We show that if X is an infinite-dimensional Banach space in which every finite-dimensional subspace is λ-complemented with λ ≤ 2 then X is (1 + C√(λ-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.},
author = {N. J. Kalton},
journal = {Studia Mathematica},
keywords = {complemented subspace theorem; perturbation of Hilbert spaces; Dvoretzky's theorem; Hilbert enlargement; reflection},
language = {eng},
number = {3},
pages = {223-257},
title = {The complemented subspace problem revisited},
url = {http://eudml.org/doc/284930},
volume = {188},
year = {2008},
}

TY - JOUR
AU - N. J. Kalton
TI - The complemented subspace problem revisited
JO - Studia Mathematica
PY - 2008
VL - 188
IS - 3
SP - 223
EP - 257
AB - We show that if X is an infinite-dimensional Banach space in which every finite-dimensional subspace is λ-complemented with λ ≤ 2 then X is (1 + C√(λ-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.
LA - eng
KW - complemented subspace theorem; perturbation of Hilbert spaces; Dvoretzky's theorem; Hilbert enlargement; reflection
UR - http://eudml.org/doc/284930
ER -