The complemented subspace problem revisited

Volume 188 / 2008

N. J. Kalton Studia Mathematica 188 (2008), 223-257 MSC: Primary 46B03, 46B20. DOI: 10.4064/sm188-3-2


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.


  • N. J. KaltonDepartment of Mathematics
    University of Missouri-Columbia
    Columbia, MO 65211, U.S.A.

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