Functional analysis
Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q
Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 661-665.

We prove that if $1≤p,q≤∞$, then the spaces $Lp+Lq$ and $Lp∩Lq$ are isomorphic if and only if $p=q$. In particular, $L2+L∞$ and $L2∩L∞$ are not isomorphic, which is an answer to a question formulated in [2].

Nous prouvons que si $1≤p,q≤∞$, alors les espaces $Lp+Lq$ et $Lp∩Lq$ sont isomorphes si et seulement si $p=q$. En particulier, $L2+L∞$ et $L2∩L∞$ ne sont pas isomorphes, ce qui est une réponse à une question formulée dans [2].

Accepted:
Published online:
DOI: 10.1016/j.crma.2018.04.019

Sergey V. Astashkin 1; Lech Maligranda 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
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Sergey V. Astashkin; Lech Maligranda. Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q. Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 661-665. doi : 10.1016/j.crma.2018.04.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.04.019/

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