Sur Certains Sous-Espaces Vectoriels De Lp

A. Grothendieck

doi:10.4153/CJM-1954-017-x

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Le théoréme qui suit résoud une question qui m'avait été posée indépendamment par M. H. Mirkil et Professeur E. Farah, dans le cas particulier de p = 2 :

Théorème 1. Soit M un espace localement compact muni d'une mesure bornée μ, et soit 1 ≤ p < + ∞. Soit H un sous-espace vectoriel de L∞(μ), fermé dans LP(μ). Alors H est de dimension finie.

References

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2. Grothendieck, A., Sur les applications linéaires faiblement compactes d'espaces du type C(K). Can. J. Math., 5 (1953), 129–173.Google Scholar

3. Zygmund, A., Trigonometrical series (Varsovie, 1935).Google Scholar

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