Some embeddings for phi.
Jesús M. Fernández Castillo (1989)
Extracta Mathematicae
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Jesús M. Fernández Castillo (1989)
Extracta Mathematicae
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Jesús M. Fernández Castillo (1992)
Collectanea Mathematica
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N. J. Kalton (2008)
Studia Mathematica
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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.
Haskell Rosenthal (1970)
Studia Mathematica
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Iryna Banakh, Taras Banakh, Katsuhisa Koshino (2013)
Bulletin of the Polish Academy of Sciences. Mathematics
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Erhard Luft (1968)
Czechoslovak Mathematical Journal
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Krishnamurthy, V.
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Juan Margalef Roig, Enrique Outerelo Domínguez (1980)
Revista Matemática Hispanoamericana
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