The complemented subspace problem revisited

• Autorzy: N. J. Kalton
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 188
• Numer: 3
• Strony: 223-257

Daty

wydano

2008

Twórcy

autor

N. J. Kalton

• Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, U.S.A.

Identyfikatory

DOI

10.4064/sm188-3-2