Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q

Astashkin, Sergey V.; Maligranda, Lech

doi:10.1016/j.crma.2018.04.019

Functional analysis

L_p + L_q and L_p ∩ L_q are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q
[L_p + L_q et L_p ∩ L_q ne sont pas isomorphes pour tout 1 ≤ p,q ≤ ∞, p ≠ q]

Présenté par : Gilles Pisier

Astashkin, Sergey V.¹ ; Maligranda, Lech ²

¹ Department of Mathematics, Samara National Research University, Moskovskoye shosse 34, 443086, Samara, Russia
² Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden

Comptes Rendus. Mathématique, Tome 356 (2018) no. 6, pp. 661-665.

Résumé
Abstract

Nous prouvons que si $1 \leq p, q \leq \infty$ , alors les espaces $L_{p} + L_{q}$ et $L_{p} \cap L_{q}$ sont isomorphes si et seulement si $p = q$ . En particulier, $L_{2} + L_{\infty}$ et $L_{2} \cap L_{\infty}$ ne sont pas isomorphes, ce qui est une réponse à une question formulée dans [2].

We prove that if $1 \leq p, q \leq \infty$ , then the spaces $L_{p} + L_{q}$ and $L_{p} \cap L_{q}$ are isomorphic if and only if $p = q$ . In particular, $L_{2} + L_{\infty}$ and $L_{2} \cap L_{\infty}$ are not isomorphic, which is an answer to a question formulated in [2].

Reçu le : 2018-03-08
Accepté le : 2018-04-17
Publié le : 2018-04-30

DOI : 10.1016/j.crma.2018.04.019

Affiliations des auteurs :

Astashkin, Sergey V. ¹ ; Maligranda, Lech ²

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     journal = {Comptes Rendus. Math\'ematique},
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Astashkin, Sergey V.; Maligranda, Lech. L_p + L_q and L_p ∩ L_q are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q. Comptes Rendus. Mathématique, Tome 356 (2018) no. 6, pp. 661-665. doi : 10.1016/j.crma.2018.04.019. http://archive.numdam.org/articles/10.1016/j.crma.2018.04.019/

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