Abstract:A result of G. Godefroy asserts that a Banach space X contains an isomorphic copy of 1 if and only if there is an equivalent norm ||| • ||| such that, for every finite-dimensional subspace Y of X and every ε > 0, there exists x ∈ S X so that |||y +rx||| ≥ (1−ε)(|||y|||+|r|) for every y ∈ Y and every r ∈ R. In this paper we generalise this result to larger cardinals, showing that if κ is an uncountable cardinal, then a Banach space X contains a copy of 1 (κ) if and only if there is an equivalent norm ||| • ||| … Show more
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