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

1. Banach, S., Théorie des opérations linéaires (Varsovie, 1932).Google Scholar

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

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Grothendieck, A. 1955. Une Caracterisation Vectorielle-Metrique Des Espaces L1. Canadian Journal of Mathematics, Vol. 7, Issue. , p. 552.

Amemiya, Ichiro 1957. Some examples of $\left( F \right)$ and $\left( {DF} \right)$ spaces. Proceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 33, Issue. 4,

Noureddine, Khalil 1976. Note Sur les EspacesD b. Mathematische Annalen, Vol. 219, Issue. 2, p. 97.

Coffman, C. V. Marcus, M. M. and Mizel, V. J. 1976. Boundary value problems for nonuniformly elliptic equations with measurable coefficients. Annali di Matematica Pura ed Applicata, Vol. 110, Issue. 1, p. 223.

Dazord, Jean 1976. Factoring operators throughc 0. Mathematische Annalen, Vol. 220, Issue. 2, p. 105.

Kalton, N. J. 1980. Subalgebras of Orlicz spaces and related algebras of analytic functions. Arkiv för Matematik, Vol. 18, Issue. 1-2, p. 223.

Khurana, Surjit Singh 1980. Weak sequential convergence in 𝐿_{𝐸}^{∞} and Dunford-Pettis property of 𝐿_{𝐸}¹. Proceedings of the American Mathematical Society, Vol. 78, Issue. 1, p. 85.

Асташкин, Сергей Владимирович and Astashkin, Sergei Vladimirovich 1999. О дизъюнктной строгой сингулярности вложений симметричных пространств. Математические заметки, Vol. 65, Issue. 1, p. 3.

Astashkin, S. V. 1999. Disjointly strictly singular inclusions of symmetric spaces. Mathematical Notes, Vol. 65, Issue. 1, p. 3.

Guo, Kunyu and Zheng, Dechao 2001. Invariant Subspaces, Quasi-invariant Subspaces, and Hankel Operators. Journal of Functional Analysis, Vol. 187, Issue. 2, p. 308.

Новиков, Сергей Яковлевич Novikov, Sergey Yakovlevich Семeнов, Евгений Михайлович Semenov, Evgenii Mikhailovich Эрнандес, Франциско Л and Hernandez, F L 2002. Строго сингулярные вложения. Функциональный анализ и его приложения, Vol. 36, Issue. 1, p. 85.

Oikhberg, Timur and Spinu, Eugeniu 2014. Operator Ideals on Non-commutative Function Spaces. Integral Equations and Operator Theory, Vol. 79, Issue. 4, p. 507.

Astashkin, Sergey and Maligranda, Lech 2018. 𝐿_{𝑝}+𝐿_{∞} and 𝐿_{𝑝}∩𝐿_{∞} are not isomorphic for all 1≤𝑝<∞, 𝑝≠2. Proceedings of the American Mathematical Society, Vol. 146, Issue. 5, p. 2181.

Manzano, Antonio Rueda, Pilar and Sánchez‐Pérez, Enrique A. 2020. Closed injective ideals of multilinear operators, related measures and interpolation. Mathematische Nachrichten, Vol. 293, Issue. 3, p. 510.

Balinsky, Alexander A. and Prykarpatski, Anatolij K. 2021. On the Finite Dimensionality of Closed Subspaces in Lp(M, dμ) ∩ Lq(M, dν). Axioms, Vol. 10, Issue. 4, p. 275.

Chen, Bo-Yong and Zhang, Liyou 2022. On the p-Bergman theory. Advances in Mathematics, Vol. 405, Issue. , p. 108516.

KAYA, Yasin 2022. On Closed Subspaces of Grand Lebesgue Spaces. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, Vol. 11, Issue. 4, p. 1014.

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