TY - JOUR

T1 - Pyramidal vectors and smooth functions on Banach spaces

AU - Deville, R.

AU - Matheron, E.

PY - 2000

Y1 - 2000

N2 - We prove that if X, Y are Banach spaces such that Y has nontrivial cotype and X has trivial cotype, then smooth functions from X into Y have a kind of "harmonic" behaviour. More precisely, we show that if Ω is a bounded open subset of X and f : Ω̄ → Y is C
1-smooth with uniformly continuous Fréchet derivative, then f(∂Ω) is dense in f(Ω̄). We also give a short proof of a recent result of P. Hájek.

AB - We prove that if X, Y are Banach spaces such that Y has nontrivial cotype and X has trivial cotype, then smooth functions from X into Y have a kind of "harmonic" behaviour. More precisely, we show that if Ω is a bounded open subset of X and f : Ω̄ → Y is C
1-smooth with uniformly continuous Fréchet derivative, then f(∂Ω) is dense in f(Ω̄). We also give a short proof of a recent result of P. Hájek.

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U2 - 10.1090/S0002-9939-00-05519-2

DO - 10.1090/S0002-9939-00-05519-2

M3 - Article

SN - 0002-9939

VL - 128

SP - 3601

EP - 3608

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 12

ER -